Question

How many balls of radius 1cm can be made from a sphere of radius 10cm?

Answer 1

Hint: In these types of questions, find the volume of the larger entity and the smaller one and divide the smaller one from the larger one to get the number of entities.

In this question, we have a ball of radius 10cm using which we are supposed to form 1cm balls.
Since the balls are given to spherical, therefore,
Volume of sphere $ = \dfrac{4}{3}\pi \times {r^3}$
Volume of ball with radius 10cm $ = \dfrac{4}{3}\pi \times {10^3}$
Volume of ball with radius 1cm$ = \dfrac{4}{3}\pi \times {1^3}$
Number of balls = $\dfrac{{Volume\,of\,sphere\,of\,radius\,10cm}}{{Volume\,of\,sphere\,of\,radius\,1cm}}$
 $ = \dfrac{{\dfrac{4}{3}\pi \times {{10}^3}}}{{\dfrac{4}{3}\pi \times {1^3}}}$
On cancelling out the common terms,
Number of balls = 1000
Answer = 1000 balls can be formed using the 10cm ball.

Note: In these type questions, make sure you take the volume as the other entities will change the value but volume will remain the same.