Volume Formulas | List of Volume Formulas You Should Know - BYJUS

# Volume Formulas

The volume formulas in mathematics are used to determine the total space occupied by any three-dimensional (3-D) object. Tennis balls, dice, and even our favorite ice cream cones are some of the examples of 3D objects. Now, let's go over the volume formulas for a few 3-D shapes in depth....Read MoreRead Less

### What is the Formula for Volume?

The formula for volume is used to figure out how much space an object can hold or contain. The volume of any three-dimensional shape is measured in ‘units$$^3$$’ or cubic units. We have different 3-D objects in math such as cubes, cuboids, spheres, hemispheres, cones, cylinders, prisms, and pyramids.

So, before determining the volume of any three dimensional object, it is better to have a proper idea of its formula. The volume formula for each shape is clearly shown in the table below.

### Solved Examples

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.