Question

The number of balls of radius 1 cm that can be made from a sphere of radius 10 cm will be:-
A) 1000
b) 10000
c) 100000
d) 100

Answer 1

Hint: In order to solve this question, the number of balls can be calculated as:-
The volume of a sphere of a radius of 10 cm = (number of balls of radius 1 cm) X (Volume of spherical balls with radius 1 cm).
Following the above equation, we will get our final result.

Complete step by step solution:
The radius of the smaller ball =1 cm;
The radius of the large ball or the sphere =10 cm
So, we know that:-
Volume of solid sphere with ‘r ‘radius $=\dfrac{4}{3}\left( \pi {{r}^{3}} \right)$ .………..①
So, the volume of solid sphere with radius 10 cm :
$=\dfrac{4}{3}\left( \pi \ {{\left( 10\text{cm} \right)}^{3}} \right)$
$=\dfrac{4}{3}\pi {{\left( 10\text{cm} \right)}^{3}}$ ………….②
And, the volume of solid spherical ball with radius 1cm is given by:-
$=\dfrac{4}{3}\left( \pi {{\left( 1\text{cm} \right)}^{3}} \right)$
$=\dfrac{4}{3}\left( \pi {{\left( 1\text{cm} \right)}^{3}} \right)$ …………..③
Let, n ball of each of radius 1cm could be made from the’ solid sphere’
Therefore ;
 From equation ② and ③, we get;
$=\dfrac{4}{3}\left\{ \pi \left( {{10}^{3}} \right) \right\}=n\times \dfrac{4}{3}\left\{ \pi {{\left( 1 \right)}^{3}} \right\}$
$=10\times 10\times 10=n\ \left( 1\times 1\times 1 \right)$
$=n=\dfrac{10\times 10\times 10}{1\times 1\times 1}$
$=n=1000$
The number of balls is 1000.
Hence, $1000$ ball of radius 1 cm can be made from a ’solid sphere of radius 10 cm’
Therefore, option (a) is the correct answer to this question.

Note: The volume here depends on the diameter of the radius of the sphere since if we take the cross-section of the sphere, it is a circle. The surface area of the sphere is the area or region of its outer surface. To calculate the sphere volume, whose radius is ‘r’ we have the below formula:
Volume of the sphere is $\Rightarrow v=\dfrac{4}{3}\pi {{r}^{3}};$
where ‘r’ is the radius of the sphere.