Question

A solid metal ball of radius 8 cm melted and recasted into smaller balls each of radius 2 cm. Find the number of such balls.

Answer 1

Step-by-step explanation:

8 divided by 2 equal to 4 , hence 4 smaller balls

Answer 2

The number of smaller balls will be 64.

Step-by-step explanation:

• Radius of the single large solid ball (R) = 8 cm
• Radius of the each smaller solid ball (r) = 2 cm
• Let n smaller balls obtained from the large solid ball.

Now, the volume of the large ball will be equal to the volume of the n smaller balls.

• ∴ volume of the large ball = n × volume of the smaller ball
• ∴      $\dfrac{4}{3}$ × $\pi$ × $R^{3}$  = n × $\dfrac{4}{3}$ × $\pi$ × $r^{3}$
•                      n  = $\dfrac{R^{3}}{r^{3}}$
•                      n = $\dfrac{8^{3}}{2^{3}}$
•                   ∴ n = 64

So,the number of smaller balls will be 64.