Question

What is the number of balls with radius 1 cm made from a solid sphere of radius 4 cm ?

Answer 1

Answer:

Radius of sphere, R=4 cm

Radius of ball, r=1 cm

Volume of sphere V

1

=

3

4

πR

3

=

3

4

π(4)

3

Volome of ball V

2

=

3

4

πr

3

=

3

4

π(1)

3

Number of balls that can made are =

V

2

V

1

=

3

4

π(1)

3

3

4

π(4)

3

=4

3

=64

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Answer 2

Given :

• Radius of solid sphere = 4cm
• Radius of ball = 1cm

To find :

Number of balls that can be made from solid sphere

Formula used :

Volume of sphere = (4/3)πr³

Procedure :

• As we want to make ball from solid sphere, Volume will remain constant
• Put Volume of solid sphere = Volume of ball × number of ball

Solution :

◈ Volume of solid sphere = (4/3) π × (4³) cm³

◈ Volume of one ball = (4/3) π × (1³) cm³

Let , number of ball = n

➠ Volume of solid sphere = n×(Volume of one ball)

$\sf \implies \dfrac{4}{3} \pi \times 64 = n \times \dfrac{4}{3} \pi \times 1 \\ \\ \sf \implies \: n \: = \dfrac{4\pi \: \times 64}{3} \: \times \dfrac{3}{4 \pi} \\ \\ \sf \implies \bold{n = 64}$

ANSWER :

Number of ball (n) = 64