Volume Formulas

Example 1:

Ron bought a brand-new toy ball with a radius of 4 inches for his brother Chris. Find the volume of this ball.

Solution:

Given, the radius of the football, \(r=4\) inches.

As we know, the shape of a ball is a sphere. 

So to find the volume of the ball, let’s use the formula to determine the volume of a sphere.

That is,

\(V=\frac{4}{3}\mathrm{\Pi}r^3\)

\(=\frac{4}{3}\times3.14\times{(4)}^3\)

\(=\frac{4}{3}\times3.14\times64\)

\(=\frac{4}{3}\times200.96\)

\(=\frac{803.84}{3}\)

\(=\) 267.94 inch\(^3\)

Therefore, the volume of Chris’s toy ball is 267.94 cubic inches.

Example 2:
If the volume of a prism is 36 meter\(^3\) and the base area is 4 meter\(^2\), then, what would be the height of the prism?

Solution:
As stated, the volume of a prism V = 36 meter\(^3\) and the base area is 4 meter\(^2\).

From the given data we can find the height of the prism using the formula:

V = area of base x height

36 = 4 x height

\(\frac{36}{4}\) = height

9 = height

Hence, the height of the prism is 9 meters.

Example 3:
Camila wants to present her mother with a nice book. She found an empty cardboard box in the store room and thoughtfully decorated it to use as a gift box for the book. But Camila is unsure whether the book which has the volume of 180 units \(^3\) will fit in the box or not. Can Camila fit the book in the box that has the dimensions of \(10\times6\times5\)?

Solution:
It is stated that the dimensions of the box are \(10\times6\times5\).

From this we can say that the box is in the shape of a cuboid.

So, the dimensions can be written as l = 10, b = 6, and h = 5.

We can find the quantity the box can contain by calculating its volume.

So, the formula for the volume of a cuboid is:

V = lbh

= \(10\times6\times5\)

= \(60\times5\)

= 300

Therefore, the volume of the box is 300 units\(^3\).

Since, the volume of the book is 180 units\(^3\), Camila can use the box as a gift box for the book.