Selina Solutions Concise Maths Class 10 Chapter 20 Cylinder, Cone and Sphere (Surface Area and Volume) Exercise 20(C)

A sphere is a solid obtained on revolving a circle about any diameter of it. So, this exercise deals with problems of finding the surface area and volume of spheres, spherical shells and hemispheres. For students wanting clarity in solving problems, the Selina Solutions for Class 10 Maths is all one needs. The solutions are at par with the latest ICSE marking schemes. Further, the Concise Selina Solutions for Class 10 Maths Chapter 20 Cylinder, Cone and Sphere (Surface Area and Volume) Exercise 20(C) PDF can be accessed in the links given below.

Selina Solutions Concise Maths Class 10 Chapter 20 Cylinder, Cone and Sphere (Surface Area and Volume) Exercise 20(C) Download PDF

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Access Selina Solutions Concise Maths Class 10 Chapter 20 Cylinder, Cone and Sphere (Surface Area and Volume) Exercise 20(C)

1. The surface area of a sphere is 2464 cm², find its volume.

Solution:

Given,

Surface area of the sphere = 2464 cm²

Let the radius of the sphere be r.

Then, surface area of the sphere = 4πr²

4πr² = 2464

4 x 22/7 x r² = 2464

r² = (2464 x 7)/ (4 x 22) = 196

r = 14 cm

So, volume = 4/3 πr³

= 4/3 x 22/7 x 14 x 14 x 14

= 11498.67 cm³

2. The volume of a sphere is 38808 cm³; find its diameter and the surface area.

Solution:

Given,

Volume of the sphere = 38808 cm³

Let the radius of the sphere = r

4/3 πr³ = 38808

4/3 x (22/7) x r³ = 38808

r³ = (38808 x 7 x 3)/ (4 x 22) = 9261

r = 21 cm

So, the diameter = 2r = 21 x 2 = 42 cm

And,

Surface area = 4πr² = 4 x 22/7 x 21 x 21 cm² = 5544 cm²

3. A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?

Solution:

Let the radius of the spherical ball = r

So, the volume = 4/3 πr³

And, the radius of smaller ball = r/2

Volume of smaller ball = 4/3 π(r/2)³ = 4/3 πr³/8 = πr³/6

Thus, the number of balls made out of the given ball = (4/3 πr³)/ (πr³/6)

= 4/3 x 6 = 8

4. How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm.

Solution:

Given,

Diameter of bigger ball = 8 cm

So, radius of bigger ball = 4 cm

Volume = 4/3 πr³ = 4/3 π 4³ = 265π/3 cm³

Radius of small ball = 1 cm

Then, volume = 4/3 πr³ = 4/3 π 1³ = 4π/3 cm³

Thus,

The number of balls = (265π/3)/ (4π/3)

= 256π/3 x 3/4π

= 64

5. 8 metallic sphere; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.

Solution:

Radius of metallic sphere = 2mm = 1/5 cm

Volume = 4/3 πr³ = 4/3 x 22/7 x 1/5 x 1/5 x 1/5 = 88/ (21 x 125) cm³

Volume of 8 spheres = (88 x 8)/ (21 x 125) = 704/ (21 x 125) cm³ ….. (i)

Let the radius of new sphere = R

Volume = 4/3 πR³ = 4/3 x 22/7 x R³ …… (ii)

According the question, equating (i) and (ii) we have

704/ (21 x 125) = 4/3 x 22/7 x R³

704/ (21 x 125) = 88/21 x R³

R³ = (704 x 21)/ (21 x 125 x 88) = 8/125

R = 2/5 = 0.4 cm = 4 mm

Therefore, the radius of the new sphere is 4 mm.

6. The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their:

(i) radii

(ii) surface areas

Solution:

Given,

The volume of first sphere = 27 x volume of second sphere

Let the radius of the first sphere = r₁

And, radius of second sphere = r₂

(i) Then, according to the question we have

4/3 πr₁³ = 27 (4/3 πr₂³)

r₁³/ r₂³ = 27

r₁/ r₂ = 3/ 1

Thus, r₁: r₂ = 3: 1

(ii) Surface area of the first sphere = 4 πr₁²

And the surface area of second sphere = 4 πr₂²

Ratio of their surface areas = 4 πr₁²/ 4 πr₂² = r₁²/ r₂² = 3²/ 1² = 9

Hence, the ratio = 9: 1