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

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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.



Rapid Recall


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.



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,












\(=\) 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?


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 \(10\times6\times5\)?


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.

Frequently Asked Questions

The relation between a prism and a pyramid is when a prism and pyramid have the same base and height, the volume of a pyramid is equal to 1/3 of the volume of the prism.

A sphere is a circular shaped ball that has a diameter or radius. However, a hemisphere is half of a sphere. Hence, the volume of a hemisphere will be half of the volume of the sphere.

The pyramids of Egypt, tents, cell phone towers, a piece of a watermelon and so on are some of the examples of pyramids.

Both prisms and pyramids are three dimensional objects that have flat-faces and bases. However, a pyramid has only one polygonal base, but a prism has two identical bases.

The volume of a cone equals one-third the volume of a cylinder that has the same radius and height of the cone.