How many balls each of radius 1cm, can be made from a solid sphere of lead of radius 8cm?
VerifiedHint: First find the volume of the solid sphere and later find the volume of one ball by using the given radius in the question. To find the number of balls divide the volume of the solid sphere by volume of one ball.
Complete step by step answer:
As, it is given that the radius of the solid sphere is R = 8cm.
And we know that the volume of solid sphere is $\dfrac{4}{3}\pi {R^3}$ where R is the radius of solid sphere. So, volume of given Solid sphere will be,
$ \Rightarrow$ Volume of Solid sphere= ${\text{ }}\dfrac{4}{3}\pi {R^3} = \dfrac{4}{3}\pi {\left( 8 \right)^3} = \dfrac{{2048\pi }}{3}c{m^3} $
The radius of the ball is given as, r = 1cm.
So, volume of one ball will be,
$\Rightarrow$ Volume of one ball = ${\text{ }}\dfrac{4}{3}\pi {r^3} = \dfrac{4}{3}\pi {\left( 1 \right)^3} = \dfrac{{4\pi }}{3}c{m^3}$
So, it is clear that number of balls that can be made is equal to,
$\Rightarrow$ Number of balls= $\dfrac{{{\text{Volume of Solid sphere}}}}{{{\text{Volume of one ball}}}}{\text{ }} = {\text{ }}\dfrac{{\dfrac{{2048\pi }}{3}c{m^3}}}{{\dfrac{{4\pi }}{3}c{m^3}}} = 512{\text{ balls}}{\text{.}} $
So, the number of balls that can be made from a given solid sphere is 512 balls.
NOTE: - Whenever we come up with this type of problem then the best way is to find the total volume/area and then divide it by volume/area of 1 ball, as per required.
