RD SHARMA Solutions for Class 9 Maths Chapter 18 - Surface Areas and Volume of a Cuboid and Cube
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Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise Ex. 18.1
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require?
Solution 4
Question 5
Solution 5
Question 6
Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the titles, if the cost of tiles is Rs. 360 per dozen.
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Ravish wanted to make a temporary shelter for his car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m x 3m?
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
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
Question 13
An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48m, 1.16 m and 8.3 dm. Find the cost of painting the inner surface at Rs 50 per sq meter.
Solution 13
Question 14
Solution 14
Question 15
The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
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.
= [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 = 937.5nn = 100
Thus, 100 bricks can be painted out by the container.
Question 16
Solution 16
Question 17
The cost of preparing the walls of a room 12 m long at the rate of Rs 1.35 per square meter is Rs 340.20 and the cost of matting the floor at 85 paise per square meter is Rs 91.80. Find the height of the room.
Solution 17
Question 18
Solution 18
Question 19
A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm. The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2, find the total expenses required for polishing and painting the surface of the bookshelf.
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
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
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 cm2Cost 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
Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise Ex. 18.2
Question 1
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How, many litres of water can it holds?
Solution 1
Volume of tank = l 
b h = (6 5 4.5) m3 = 135 m3
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.
1 m3 = 1000 litres
Thus, the tank can hold 135000 litres of water.
Question 2
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
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
l 
b h = 380
Length (l) of vessel = 10 m
Width (b) of vessel = 8 m
Volume of vessel = 380 m3
l b h = 380 10
8 h = 380 h = 4.75
Thus, the height of the vessel should be 4.75 m.
Question 3
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m3.
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 (14430) = Rs 4320
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 4320Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?
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.
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.
Question 17
A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in fig. If the edge of each cube is 3 cm, find the volume of the structure built by the child
Solution 17
Question 18
A godown measures 40 m 
25 m 10 m. Find the maximum number of wooden crates each measuring 1.5 m 1.25 m 0.5 m that can be stored in the godown.
25 m 10 m. Find the maximum number of wooden crates each measuring 1.5 m 1.25 m 0.5 m that can be stored in the godown. 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
of the godown = 40 mBreadth
of the godown = 25 mHeight
of the godown = 10 mVolume of godown = l1
b1 h1 = (40 25 10) = 10000 Length
of a wooden crate = 1.5 mBreadth
of a wooden crate = 1.25 mHeight
of a wooden crate = 0.5 mVolume 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.
Question 19
A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm x 12 cm x 8 cm, how many bricks would be required?
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22
A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
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.
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. Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 26
A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water upto 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.
Solution 26
Question 27
Solution 27
Question 28
Solution 28
Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise 18.35
Question 1
Solution 1
Question 2
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is
(a) 7 : 9
(b) 49 : 81
(c) 9 : 7
(d) 27 : 23
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48 cm3, the total surface area of the box is
(a) 27 cm2
(b) 32 cm2
(c) 44 cm2
(d) 88 cm2
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).
Question 7
If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and the volume is 9000 cm3, then the length of the shortest edge is
(a) 30 cm
(b) 20 cm
(c) 15 cm
(d) 10 cm
Solution 7
Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise 18.36
Question 8
If each edge of a cube, of volume V, is doubled, then the volume of the new cube is
(a) 2 V
(b) 4 V
(c) 6 V
(d) 8 V
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).
Question 9
If each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is
(a) 2 S
(b) 4 S
(c) 6 S
(d) 8 S
Solution 9
Question 10
The area of the floor of a room is 15 m2. If its height is 4 m, then the volume of the air contained in the room is
(a) 60 dm3
(b) 600 dm3
(c) 6000 dm3
(d) 60000 dm3
Solution 10
Question 11
The cost of constructing a wall 8 m long, 4 m high and 20 cm thick at the rate of Rs. 25 per m3 is
(a) Rs. 16
(b) Rs. 80
(c) Rs. 160
(d) Rs. 320
Solution 11
Question 12
10 cubic metres clay is uniformly spread on a land of area 10 ares. The rise in the level of the ground is
(a) 1 cm
(b) 10 cm
(c) 100 cm
(d) 1000 cm
Solution 12
Question 13
Volume of a cuboid is 12 cm3. The volume (in cm3) of a cuboid whose sides are double of the above cuboid is
(a) 24
(b) 48
(c) 72
(d) 96
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).
Question 14
If the sum of all the edges of a cube is 36 cm, then the volume (in cm3) of that cube is
(a) 9
(b) 27
(c) 219
(d) 729
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).
Question 15
The number of cubes of sides 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is
(a) 9
(b) 10
(c) 18
(d) 20
Solution 15
Question 16
On a particular day, the rain fall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is
(a) 300 litres
(b) 450 litres
(c) 3000 litres
(d) 4500 litres
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
If each edge of a cube is increased by 50%, the percentage increase in its surface area is
(a) 50%
(b) 75%
(c) 100%
(d) 125%
Solution 21
Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise 18.37
Question 22
A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm3. The two cubes are then placed on top of a third cube whose volume is 8 cm3. The height of the stacked cubes is
(a) 3.5 cm
(b) 3 cm
(c) 7 cm
(d) none of these
Solution 22
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