Question

A solid metallic sphere of radius 8 cm is melted and recasted into spherical solid balls each of radius 1 cm. Then, the

number of solid balls is

a)500
b) 510
c)512
d) 516​

Answer 1

Step-by-step explanation:

Given:-

• Radius of metallic sphere = 8cm

• The metallic sphere is recasted into a spherical solid balls each of radius 1cm.

To Find:-

• The Number of solid balls.

Solution:-

Radius of the sphere (R) = 8cm

Volume of the sphere = $\rm \dfrac{4}{3} \pi {r}^{3}$

$= \rm \dfrac{4}{3} \pi \times {(8)}^{3}$

$= \rm \dfrac{4}{3} \pi \times 512$

$\rm Volume \: of \: the \: larger \: sphere = \dfrac{4}{3} \pi \times 512$

Radius of smaller metallic ball (r) = 1cm

Volume of the metallic ball = $\rm \dfrac{4}{3} \pi {r}^{3}$

$= \rm \dfrac{4}{3} \pi\times {1}^{3}$

= $= \rm \dfrac{4}{3} \pi$

$\rm Volume \: of \: the \: smaller \: sphere = \dfrac{4}{3} \pi$

$\rm Number \: of \: metallic \: balls = \dfrac{Volume\: of \: larger\: sphere}{Volume\: of \: smaller \: sphere}$

$\rm = \dfrac{ \dfrac{4}{3} \pi \times 512}{ \dfrac{4}{3}\pi } = 512$

$\underline{ \boxed{ \therefore\textsf{ \textbf{ \purple{Number of solid balls = 512}}}}}$