Question

The diameter of volleyball is $8.15$ inches. What is the volume of the ball?

Answer 1

Hint: Here we have to find the volume of the volleyball as we can visualize that volleyball is in the shape of a sphere. So our first step will be to find the radius of the volleyball by the value of diameter given. Then we will use the formula of volume of a sphere and substitute all the values in it and solve it to get our desired answer.

Complete step-by-step solution:
It is given to us that we have to find the volume of a volleyball whose diameter is $8.15$ inches.

As we can visualize that volleyball is in shape of a Sphere and Volume of Sphere is calculated by the below formula:
$V = \dfrac{4}{3}\pi {r^3}$……$\left( 1 \right)$
Where $r = $ Radius
The diameter of the volleyball is as follows:
$d = 8.15$inches …..$\left( 2 \right)$
The formula of Radius is as follows:
$r = \dfrac{d}{2}$
Substitute the value from (2) in above formula we get,
$r = \dfrac{{8.15}}{2}$
$ \Rightarrow r = 4.075$ inches
Substitute the above value in equation (1) as follows:
$V = \dfrac{4}{3}\pi \times {\left( {4.075} \right)^3}i{n^3}$
$ \Rightarrow V = \dfrac{4}{3} \times \dfrac{{22}}{7} \times {\left( {4.075} \right)^3}i{n^3}$
On simplifying the above value we get,
$V \approx 283.56\,i{n^3}$
So we get the volume of the volleyball as $283.56\,i{n^3}$ .

Note: A sphere is a three-dimensional round-shaped geometrical object. It is similar to a circle as it is also mathematically defined as the set of points that are all at the same distance from a given point but in a three-dimensional space. The sphere is a three-dimensional object that is why it also has a volume and a surface area.