Question

The diameter of a solid metallic sphere is 16cm.the sphere is melted and recast into 8 equal solid spherical balls.determine the radius of the balls

Answer 1

$volume \: of \: sphere \\ = \frac{4}{3} \pi \times { (\frac{16}{2} )}^{3} \\ let \: the \: radius \: of \: balls \: be \: r \\ then$
$8 \times \frac{4}{3} \pi \times {r}^{3} = \frac{4}{3} \pi \times {8}^{3} \\ {r}^{3} = 64 = {4}^{3} \\ thus \: radius \: of \: balls \: = 4 \: cm$

Answer 2

Given:

Diameter of the big sphere = 16 cm

Number of small balls needed = 8

To Find:

Radius of the ball

Solution

Find the volume of the sphere:

Volume of the sphere = 4/3 πr³

Volume of the sphere = 4/3 π(16 ÷ 2)³

Volume of the sphere = 2048π/3 cm³

Find the volume of small ball:

8 balls = 2048π/3 cm³

1 ball =  2048π/3  ÷ 8

1 ball = 256π/3 cm³

Find the radius:

Volume of the sphere = 4/3 πr³

4/3 πr³ =  256π/3

4r³ = 256

r³ = 64

r = 4 cm

Answer: The radius is 4 cm