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Class 10 RD SHARMA Solutions Maths Chapter 14 - Surface Areas and Volumes

Surface Areas and Volumes Exercise Ex. 14.1

Solution 46

*Answer given in the book is incorrect.

Solution 65

*Answer given in the book is incorrect.

Solution 72

Height of the conical vessel h = 24 cm

Radius of the conical vessel r =5 cm

Let h be the height of the cylindrical vessel which is filled by water of the conical vessel.

Radius of the cylindrical vessel =10 cm

Volume of the cylindrical vessel = volume of water

π(10)2h=150π

h = 150π¸ 100π

h = 1.5 cm

Thus, the height of the cylindrical vessel is 1.5 cm.

Surface Areas and Volumes Exercise Ex. 14.2

Solution 38

Total area of the canvas = curved surface area of the cone + curved surface area of a cylinder radius = 28 m height (cylinder) = 6 m

height (cone) = 21 m

l = slant height of cone

curved surface area of the cone = πrl

×28×35

=×28×35 = 3080 m2

curved surface area of the cylinder = 2πrh

=2××28×6

=1056

Total area of the canvas = 3080+1056 =4136 m2

Surface Areas and Volumes Exercise Ex. 14.3

Solution 21

Let the height of the cone be H and the radius be R. This cone is divided into two equal parts.

AQ=1/2 AP

Also,

QP||PC

ThereforeAQD~ΔAPC.

So,

Solution 22

A bucket, made of metal sheet, is in the form of a cone.

R = 15 cm, r = 6 cm and H=35 cm

Now, using the similarity concept, we can writ

Volume of the frustum is

The rate of milk is Rs. 40 per litre.

So, the cost of 51.48 litres is Rs. 2059.20.

Solution 23

(i)

Given:

Radius of lower end (r1) = Diameter/2 = 5 cm

Radius of upper end (r2) = Diameter/2 = 15 cm

Height of the bucket (h) = 24 cm

Area of metal sheet used in making the bucket

= CSA of bucket + Area of smaller circular base

Hence, area of the metal sheet used in making the bucket is 1711.3 cm2.

(ii)

We should avoid the bucket made by ordinary plastic because it is less strength than metal bucket and also not ecofriendly.

Surface Areas and Volumes Exercise 14.88

Solution 1

After melting a sphere and converting it into a wire, the volume remains same.

So the correct option is (c).

Solution 2

So, the correct option is (b).

Solution 3

So the correct option is (b).

Solution 5

So, the correct option is (b).

Solution 6

So, the correct option is (d).

Solution 7

So, the correct option is (c).

Solution 8

So, the correct option is (a).

Solution 9

So, correct option is (b).

Solution 10

So, the correct option (d).

Solution 11

So, the correct option is (c).

Solution 12

So, the correct option is (b).

Surface Areas and Volumes Exercise 14.89

Solution 13

So, the correct option is (a).

Solution 14

So, the correct option is (b).

Solution 15

So, the correct option is (c).

Solution 16

So, the correct option is (d).

Solution 17

So, the correct option is (a).

Solution 18

So, the correct option is (b).

Solution 19

So, the correct option is (d).

Solution 20

So, the correct option is (d).

Solution 21

Volume of the sphere = Sum of the volume of the three spheres

So, correct option is (b).

Solution 22

So, correct option is (c).

Solution 23

So, correct option is (a).

Solution 24

So, the correct option is (c).

Surface Areas and Volumes Exercise 14.90

Solution 25

So, correct option is (d).

Solution 26

So, the correct option is (b).

Solution 27

So, the correct option is (b).

Solution 28

So, the correct option is (a).

Solution 29

Diameter = 1.6 m = 160 cm

So, the correct option is (b).

Solution 30

So, the correct option is (d).

Solution 31

So, correct option is (b).

Solution 32

So, the correct option is (a).

Solution 33

The cylinder completely encloses the sphere.

Hence, diameter of the sphere = diameter of the cylinder = 2r

Now, h is also given to be 2r.

So, the correct option is (a) or (c).

Note: Both can be the answer since h = 2r.

Solution 34

So, the correct option is (a).

Solution 35

So, the correct option is (b).

Solution 36

So, the correct option is (c).

Solution 37

So, the correct option is (c).

Surface Areas and Volumes Exercise 14.91

Solution 38

So, the correct option is (a).

Solution 39

So, the correct option is (c)

Solution 40

So, the correct option is (b).

Solution 41

So, the correct option is (c).

Solution 42

So, the correct option is (c).

Solution 43

So, the correct option is (a).

Solution 44

So, the correct option is (b).

Solution 46

Correct option: (b)

From the figure, it is clear that diameter of sphere is 2r.

Solution 47

Correct option: (a)

In a right circular cone, the cross-section made by a plane parallel to the base is a circle.

Solution 48

Correct option: (a)

When two solid-hemispheres of same base radius r are joined together along their bases, it forms a sphere.

And, CSA of sphere = 4πr2