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RD Sharma Solution for Class 9 Mathematics Chapter 18 - Surface Areas and Volume of a Cuboid and Cube

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Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 9 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 18 - Surface Areas and Volume of a Cuboid and Cube.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 9 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 9 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

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RD Sharma Solution for Class 9 Mathematics Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Page/Excercise 18.1

Solution 1

Solution 2

Solution 3

Solution 4


Solution 5

Solution 6


Solution 7

Solution 8

Solution 9


Solution 10

Solution 11

Solution 12

Length of shelter = 4 m
Breadth of shelter = 3 m
Height of shelter = 2.5 m

The tarpaulin will be required for top and four sides of the shelter.
Area of Tarpaulin required = 2(lh + bh) + lb
= [2(4  2.5 + 3 2.5) + 4 3] m2
= [2(10 + 7.5) + 12] m2
= 47 m2


Solution 13

Solution 14

Solution 15

Total surface area of one brick = 2(lb + bh + lh)
 = [2(22.5 × 10 + 10 × 7.5 + 22.5 × 7.5)]cm2
 = 2(225 + 75 + 168.75)
          = (2 × 468.75) cm2
 = 937.5 cm2   
Let n number of bricks be painted by the container.
Area of n bricks = 937.5n cm2   
Area that can be painted by the container = 9.375 m2 = 93750 cm2
 93750 = 937.5n
n = 100
Thus, 100 bricks can be painted out by the container.

 

Solution 16

Solution 17

Solution 18

Solution 19

    External length (l) of bookshelf = 85 cm
    External breadth (b) of bookshelf = 25 cm
    External height (h) of bookshelf = 110 cm
    External surface area of shelf while leaving front face of shelf
                                                  = lh + 2 (lb + bh)
                                                  = [85  110 + 2 (85 25 + 25 110)] cm2
                                                  = 19100 cm2
    Area of front face = [85 110 - 75 100 + 2 (75 5)] cm2
                                                  = 1850 + 750 cm2
                                                  = 2600 cm2
    Area to be polished = (19100 + 2600) cm2 = 21700 cm2    
    Cost of polishing 1 cm2 area = Rs 0.20
    Cost of polishing 21700 cm2 area = Rs (21700 0.20) = Rs 4340    
    
    Now, length (l), breadth (b) height (h) of each row of bookshelf is 75 cm, 20 cm, and     30cm  respectively.
    Area to be painted in 1 row = 2 (l + h) b + lh
                                           = [2 (75 + 30) 20 + 75 30] cm2
                                           = (4200 + 2250) cm2
                                           = 6450 cm2    
    Area to be painted in 3 rows = (3 6450) cm2 = 19350 cm2
    Cost of painting 1 cm2 area = Rs 0.10
    Cost of painting 19350 cm2 area = Rs (19350 0.10) = Rs 1935    
    Total expense required for polishing and painting the surface of the bookshelf                                              = Rs(4340 + 1935) = Rs 6275

RD Sharma Solution for Class 9 Mathematics Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Page/Excercise 18.2

Solution 1

Volume of tank = l  b h = (6  5 4.5) m3 = 135 m3   It is given that:
 1 m3 = 1000 litres

    
 Thus, the tank can hold 135000 litres of water.

Solution 2

Let height of cuboidal vessel be h.
Length (l) of vessel = 10 m
Width (b) of vessel = 8 m
Volume of vessel = 380 m3
  b h = 380         
 10 8 h = 380
 h = 4.75
    
 Thus, the height of the vessel should be 4.75 m.    

Solution 3

Length (l) of the cuboidal pit = 8 m
Width (b) of the cuboidal pit = 6 m
 Depth (h) of the cuboidal pit = 3 m
Volume of the cuboidal pit = l  b h = (8 6 3)  = 144 m3  
Cost of digging 1 m3 = Rs 30
Cost of digging 144 m3 = Rs (144 30) = Rs 4320

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Length (l) of the cuboidal tank = 20 m
Breadth (b) of the cuboidal tank = 15 m
Height (h) of the cuboidal tank = 6 m

Capacity of tank = l × b × h    = (20 × 15 × 6) m3 = 1800 m3 = 1800000 litres

Water consumed by people of village in 1 day = 4000 × 150 litres = 600000 litres

Let water of this tank lasts for n days.
Water consumed by all people of village in n days = capacity of tank
n × 600000 = 1800000
n = 3    
Thus, the water of tank will last for 3 days.

Solution 17

Solution 18

Length  of the godown = 40 m
    Breadth  of the godown = 25 m
    Height  of the godown = 10 m

Volume of godown = l1 b1 h1 = (40  25  10)  = 10000     

    Length  of a wooden crate = 1.5 m
    Breadth  of a wooden crate = 1.25 m
    Height  of a wooden crate = 0.5 m

Volume of a wooden crate =      = (1.5  1.25  0.5) m3 = 0.9375

Let n wooden crates be stored in the godown.
Volume of n wooden crates = volume of godown
0.9375  n = 10000
 

Thus, 10666 wooden crates can be stored in godown.

Solution 19

Solution 20

Solution 21

Solution 22

Rate of water flow = 2 km per hour  
Depth (h) of river = 3 m
Width (b) of river = 40 m
Volume of water flowed in 1 min  
Thus, in 1 minute 4000  = 4000000 litres of water will fall into the sea.    

Solution 23

Solution 24

Solution 25

Solution 26

Solution 27

Solution 28

RD Sharma Solution for Class 9 Mathematics Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Page/Excercise 18.35

Solution 1

begin mathsize 12px style The space longest space rod space that space can space be space fitted space in space straight a space cube space is space diagonal space of space straight a space cube.
Now comma space if space straight a space is space side space of space straight a space cube comma space then space diagonal space equals space square root of straight a squared plus straight a squared plus straight a squared end root equals square root of 3 straight a
rightwards double arrow Diagonal space of space straight a space cube space of space edge space 10 space cm space equals space 10 square root of 3 space cm
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style

Solution 2

begin mathsize 12px style Surface space of space one space cube space equals 6 left parenthesis edge right parenthesis squared equals space 6 straight a squared
rightwards double arrow Surface space area space of space three space cubes space equals 3 space cross times 16 straight a squared equals space 18 straight a squared
Surface space Area space of space cuboid space formed
equals 2 left parenthesis lb space plus space bh space plus space hl right parenthesis
equals 2 left parenthesis 3 straight a cross times straight a space plus space straight a cross times straight a space plus space straight a space cross times space 3 straight a right parenthesis
equals 2 left parenthesis 3 straight a squared plus straight a squared plus 3 straight a squared right parenthesis
equals 2 space cross times space 7 straight a squared
equals 14 straight a squared
rightwards double arrow Required space Ratio space equals space fraction numerator Surface space area space of space resulting space cuboid over denominator Surface space area space of space three space cubes end fraction equals fraction numerator 14 straight a squared over denominator 18 straight a squared end fraction space equals 7 over 9 equals 7 space colon space 9
Hence comma space correct space option space is space left parenthesis straight a right parenthesis. end style

Solution 3

begin mathsize 12px style Length space of space diagonal space of space straight a space cube space of space side space straight a space equals space 8 square root of 3 space cm
rightwards double arrow square root of 3 straight a space equals space space 8 square root of 3
rightwards double arrow straight a space equals space 8 space cm
So comma space Surface space Area space of space straight a space Cube space equals space 6 straight a squared equals space 6 space cross times space 8 space cross times space 8 equals 384 space cm squared space space space
Hence comma space correct space option space is space left parenthesis straight b right parenthesis. end style

Solution 4

begin mathsize 12px style If space side space of space 1 to the power of st space cube space equals space straight a space and space side space of space 2 to the power of nd space cube space equals space straight b comma space then
fraction numerator Volume space of space 1 to the power of st space cube over denominator Volume space of space 2 to the power of nd space cube end fraction space equals space straight a cubed over straight b cubed equals 8 over 1
rightwards double arrow straight a over straight b equals 2 over 1
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style

Solution 5

begin mathsize 12px style Surface space Area space of space Cube space equals space 6 straight a squared space equals space 96 space cm squared
rightwards double arrow straight a squared space equals space 16 space cm squared
rightwards double arrow straight a space equals space 4 space cm
rightwards double arrow Volume space equals space straight a cubed space equals space 4 cubed space equals space 64 space cm cubed
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style

Solution 6

Let,

Length = 3x,

Width = 2x

Height = x

Volume = 48 cm3

L×W×H = 48 cm3

3x × 2x × x = 48 cm3

6x3 = 48 cm3

x3 = 8 cm3

x = 2 cm

Total Surface area

= 2(3x × 2x + 2x × x + 3x × x)

= 2(6x2 + 2x2 + 3x2

= 2(11x2)

= 22x2

= 22(4)

= 88 cm2

Hence, correct option is (d).

Solution 7

begin mathsize 12px style Three space adjacent space Faces space are space AEHD comma space DCGH comma space EHGF
Ratio space of space areas comma
bc space colon space ac space colon space ab space equals space 2 space colon space 3 space colon space 4 space space..... open parentheses 1 close parentheses
Volume comma space abc space equals space 9000 space cm cubed
From space eq. space open parentheses 1 close parentheses comma space let space bc space equals space 2 straight x comma space space ac space equals space 3 straight x comma space space ab space equals space 4 straight x
rightwards double arrow left parenthesis 2 straight x space cross times space 3 straight x space cross times space 4 straight x right parenthesis space equals space left parenthesis bc right parenthesis left parenthesis ac right parenthesis left parenthesis ab right parenthesis
rightwards double arrow 24 straight x cubed space equals space left parenthesis abc right parenthesis squared space
rightwards double arrow 24 straight x cubed space equals space left parenthesis 9000 right parenthesis squared equals 81000000
straight x cubed space equals space fraction numerator 81 space cross times space 10 to the power of 6 over denominator 24 end fraction space equals fraction numerator 27 cross times 10 to the power of 6 over denominator 8 end fraction
rightwards double arrow space straight x space equals space fraction numerator 3 space cross times space 10 squared over denominator 2 end fraction rightwards double arrow straight x space equals space 150 space cm
rightwards double arrow bc space equals space 300 space cm squared comma space space space ac space equals space 450 space cm squared comma space space space ab space equals space 600 space cm squared
Thus comma space we space have
straight a equals abc over bc equals 9000 over 300 equals space 30 space cm comma space space straight b space equals space abc over ac equals fraction numerator begin display style 9000 end style over denominator 450 end fraction equals 20 space cm comma space space straight c space equals abc over ab equals 9000 over 600 equals 15 space cm
rightwards double arrow The space length space of space the space Shortest space edge space equals space 15 space cm.
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style

RD Sharma Solution for Class 9 Mathematics Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Page/Excercise 18.36

Solution 8

Let edge = a

Volume, V = a3

If a' = 2a, then

V' = (a')3 = (2a)3 = 8a3

V' = 8 V

Hence, correct option is (d).

Solution 9

begin mathsize 12px style Let space the space edges space of space Cuboid space be space straight a comma space straight b comma space straight c
straight S space equals space Surface space Area space equals space 2 left parenthesis ab space plus space bc space plus space ca right parenthesis
If space straight a apostrophe space equals space 2 straight a comma space space straight b apostrophe space equals space 2 straight b comma space space space straight c apostrophe space equals space 2 straight c comma space then space
straight S apostrophe space equals space 2 left parenthesis straight a apostrophe straight b apostrophe plus straight b apostrophe straight c apostrophe plus straight c apostrophe straight a apostrophe right parenthesis space
rightwards double arrow straight S apostrophe space equals space 2 left square bracket left parenthesis 2 straight a right parenthesis left parenthesis 2 straight b right parenthesis space plus space left parenthesis 2 straight b right parenthesis left parenthesis 2 straight c right parenthesis space plus space left parenthesis 2 straight c right parenthesis left parenthesis 2 straight a right parenthesis right square bracket
rightwards double arrow straight S apostrophe space equals space 2 left square bracket 4 ab space plus space 4 bc space plus space 4 ca right square bracket
rightwards double arrow straight S apostrophe equals space 4 space cross times space 2 open parentheses ab space plus space bc space plus space ca close parentheses
rightwards double arrow straight S apostrophe space equals space 4 space straight S
Hence comma space correct space option space is space left parenthesis straight b right parenthesis. end style

Solution 10

begin mathsize 12px style Volume space of space room space equals space Area space of space floor space cross times space Height space of space room
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 15 space straight m squared space cross times space 4 space straight m
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1500 space dm squared space cross times space 40 space dm
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 60000 space dm cubed
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

Solution 11

Volume space of space wall equals 8 space straight m space cross times space 4 space straight m space cross times space 20 space cm space equals 8 space straight m space cross times space 4 space straight m space cross times space 1 fifth straight m equals 32 over 5 straight m cubed
rightwards double arrow Cost space of space constructing space wall equals Rs. space open parentheses 25 space cross times space 32 over 5 close parentheses equals Rs. space 160
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. space space

Solution 12

begin mathsize 14px style Area space of space land equals 10 space ares space equals space 10 space cross times space 100 space straight m squared space equals space 1000 space straight m squared
Volume space of space clay equals 10 space straight m cubed
rightwards double arrow Area space of space land space cross times space Rise space in space level space equals space 10 space straight m cubed
rightwards double arrow 1000 space straight m squared space cross times space Rise space in space level space equals space 10 space straight m cubed
rightwards double arrow Rise space in space level space equals space fraction numerator 10 space straight m cubed over denominator 1000 space straight m squared end fraction equals 1 over 100 straight m space equals space 1 space cm
Hence comma space correct space option space is space left parenthesis straight a right parenthesis. end style

Solution 13

Let the dimensions of Cuboid be a, b, c respectively.

Volume, V = abc = 12 cm3

If a' = 2a,   b' = 2b,   c' = 2c, then 

V' = a'b'c' = 8abc = 8 × 12 = 96 cm3

Hence, correct option is (d).

Solution 14

Let the edge of cube = a

Total no. of edge = 12

Sum of all edges = 12a

12a = 36cm

i.e. a = 3 cm

Volume = a3 = 33 = 27 cm3

Hence, correct option is (b).

Solution 15

begin mathsize 12px style Volume space of space cuboid space equals space 10 space cm space cross times space 9 space cm space cross times space 6 space cm space equals space 540 space cm squared
Volume space of space Cube space equals space open parentheses 3 space cross times space 3 space cross times space 3 close parentheses space cm cubed space equals space 27 space cm cubed
No. space of space cubes space that space can space be space cut space from space straight a space cuboid space equals space 540 over 27 equals 20
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

Solution 16

begin mathsize 12px style Volume space of space water space collected space
equals space 6 space straight m space cross times space 5 space straight m space cross times space 15 over 100 straight m
equals 450 over 100 straight m cubed
equals 4.5 space straight m
equals space 4.5 space cross times space 1000 space litres space space space space space space space space space space space space space space space space space space space space space
equals space 4500 space litres space space
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

Solution 17

begin mathsize 12px style Let space three space adjacent space faces space be space ADHE comma space DCGH comma space EHGF.
straight A subscript 1 space equals space ar left parenthesis ADHE right parenthesis space equals space bc
straight A subscript 2 space equals space ar left parenthesis DCGH right parenthesis space equals space ca
straight A subscript 3 space equals space ar left parenthesis EHGH right parenthesis space equals space ab
Volume space of space cuboid space equals space abc
Now comma space space straight A subscript 1 straight A subscript 2 straight A subscript 3 space equals space bc cross times ca cross times ab space equals space straight a squared straight b squared straight c squared
Also comma space we space can space write
abc space equals space Volume space of space Cuboid space equals space square root of straight a squared straight b squared straight c squared end root equals square root of straight A subscript 1 straight A subscript 2 straight A subscript 3 end root
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style

Solution 18

begin mathsize 12px style Length space of space diagonal space of space cube space of space side space straight a space equals space square root of 3 straight a
Volume comma space straight V space equals space straight a cubed space
rightwards double arrow left parenthesis straight V right parenthesis to the power of bevelled 1 third end exponent equals space straight a
Now comma space length space of space diagonal space comma space straight l space equals space square root of 3 space left parenthesis straight V right parenthesis to the power of 1 divided by 3 end exponent
rightwards double arrow straight l cubed space equals space 3 square root of 3 space straight V
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

Solution 19

begin mathsize 12px style Sides space of space straight a space cuboid space are space straight x comma space straight y comma space straight z
Volume space equals xyz space equals space straight V
Surface space Area space equals space 2 left parenthesis xy space plus space yz space plus space zx right parenthesis space equals space straight A
straight A over straight V equals fraction numerator 2 open parentheses xy space plus space yz space plus space zx close parentheses over denominator xyz end fraction space equals space 2 open parentheses 1 over straight z plus 1 over straight x plus 1 over straight y close parentheses equals space 2 open parentheses 1 over straight x plus 1 over straight y plus 1 over straight z close parentheses
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style

Solution 20

begin mathsize 12px style If space straight a comma space straight b comma space straight c space are space the space sides space of space straight a space cuboid comma space then
straight a space plus space straight b space plus space straight c space equals space 19 space cm
Length space of space diagonal space equals space 5 square root of 5
rightwards double arrow space square root of straight a squared space plus space straight b squared space plus space straight c squared end root equals 5 square root of 5
rightwards double arrow straight a squared space plus space straight b squared space plus space straight c squared equals open parentheses 5 square root of 5 close parentheses squared equals 25 cross times 5 equals 125 space cm
Now comma space left parenthesis straight a space plus space straight b space plus space straight c right parenthesis squared space space space equals space straight a squared space plus space straight b squared space plus space straight c squared space plus space 2 left parenthesis ab space plus space bc space plus space ca right parenthesis
rightwards double arrow left parenthesis 19 right parenthesis squared space equals 125 space space plus space Surface space Area space of space Cuboid
rightwards double arrow Surface space Area space of space straight a space Cuboid space equals space 361 space minus space 125 space equals space 236 space cm squared
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style

Solution 21

begin mathsize 12px style Surface space Area space of space straight a space Cube space of space side space straight a space equals space 6 straight a squared
If space straight a space is space incresed space by space 50 percent sign comma
straight a apostrophe left parenthesis new space side right parenthesis space equals space straight a space plus space straight a over 2 equals fraction numerator 3 straight a over denominator 2 end fraction
So space new space Surface space Area space equals space straight S apostrophe space equals space 6 straight a apostrophe squared equals 6 open parentheses fraction numerator 3 straight a over denominator 2 end fraction close parentheses squared space equals space fraction numerator 6 cross times 9 cross times straight a squared over denominator 4 end fraction equals space 13.5 space straight a squared space
Increase space in space area space equals space 13.5 straight a squared space minus space 6 straight a squared equals space 7.5 straight a squared space
percent sign space Increase space equals space fraction numerator 7.5 up diagonal strike straight a squared end strike over denominator 6 up diagonal strike straight a squared end strike end fraction cross times 100 percent sign space equals space 125 percent sign
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

RD Sharma Solution for Class 9 Mathematics Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Page/Excercise 18.37

Solution 22

begin mathsize 12px style Side space of space cube space whose space volume space is space space 1 over 8 cm cubed space equals space open parentheses 1 over 8 close parentheses to the power of 1 divided by 3 end exponent space equals 1 half space cm space space space open curly brackets straight V equals space open parentheses straight a close parentheses cubed close curly brackets
Side space of space Second space cube space whose space volume space is space 1 space cm cubed space equals space open parentheses 1 close parentheses to the power of 1 divided by 3 end exponent space equals space 1 space cm
Side space of space Third space cube space whose space volume space is space 8 space cm cubed equals space open parentheses 8 close parentheses to the power of 1 divided by 3 end exponent space equals space 2 space cm
1 st space Cube space is space placed space on space second space and space second space on space third comma space
then space height space of space stacked space cubes
equals Sum space of space sides space of space all space cubes
equals space open parentheses 1 half plus space 1 space plus space 2 close parentheses space cm
equals space 3.5 space cm
Hence comma space correct space option space is space left parenthesis straight a right parenthesis. end style

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 9. Access the CBSE Class 9 Mathematics Chapter 18 - Surface Areas and Volume of a Cuboid and Cube for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 18 - Surface Areas and Volume of a Cuboid and Cube.

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