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

Given,

Diameter of bigger ball = 8 cm

So, radius of bigger ball (R) = $\dfrac{8}{2}$ = 4 cm.

Volume of bigger ball = $\dfrac{4}{3}πR^3$

= $\dfrac{4}{3} \times π (4)^3$

= $\dfrac{4}{3} \times π \times 64 = \dfrac{256π}{3} \text{ cm}^3$.

Radius of small ball (r) = 1 cm

Volume of each smaller ball = $\dfrac{4}{3}πr^3$

= $\dfrac{4}{3} \times π \times (1)^3 = \dfrac{4}{3}π \text{ cm}^3.$

Let n smaller balls can be made by, melting bigger ball.

Volume of bigger ball = n × Volume of each smaller ball

$\Rightarrow \dfrac{256π}{3} = n \times \dfrac{4}{3}π \\[1em] \Rightarrow n = \dfrac{\dfrac{256π}{3}}{\dfrac{4}{3}π} \\[1em] \Rightarrow n = \dfrac{256 \times π \times 3}{4 \times 3 \times π} \\[1em] \Rightarrow n = 64.$

Hence, 64 balls can be made.