Question

A solid iron spherical ball is melted and recast into smaller balls of equal size. If the radius of smaller ball is 1/8 th of the original ball. Find the number of smaller balls made. Assuming that there is no wastage of metal in the process.

Answer 1

Answer:

The number of smaller balls made is 512.

Step-by-step explanation:

Since we know that a solid iron spherical ball is melted and recast into smaller balls of equal size. If the radius of smaller ball is 1/8 th of the original ball, our aim is to find the number of smaller balls made. Assuming that there is no wastage of metal in the process.

Let R be the radius of the bigger ball and $\frac{R}{8}$ the radius of the smaller ball.

Thus, the number of small ball is equal to the volume of the bigger ball under the volume of the smaller ball, and is equal to:

$\frac{\frac{4}{3} (pi) R^{3} }{\frac{4}{3} (pi) \frac{R}{8} ^{3}}$

= 512 balls

Hence, the number of smaller balls made is 512.

Answer 2

Answer:

The number of smaller balls made can be calculated by dividing the volume of the big ball with the volume of one smaller ball.

Let R be the radius of the big ball and r be the radius of the small ball.

Then, volume of the big ball = 4/3 π R³ ........................... (1)

Volume of one small ball = 4/3 π r³

We know that  r = 1/8 R

or, R = 8 r

so, Volume of big ball = 4/3 π (8 r )³ = 4/3 π 512 r³ ..................... (3)

Now, the number of smaller balls = 4/3 π 512 r³ / 4/3 π r³

= 512

Hence the number of smaller balls made = 512.