OML Search

Volume Formulas




 
In these lessons, we give
  • a table of volume formulas and surface area formulas used to calculate the volume and surface area of three-dimensional geometrical shapes: cube, cuboid, prism, solid cylinder, hollow cylinder, cone, pyramid, sphere and hemisphere.
  • a more detailed explanation (in text and videos) of each volume formula.

Related Topics: More Geometry Lessons, Volume Games

Table of Volume Formulas and Surface Area Formulas

The following table gives the volume formulas for solid shapes or three-dimensional shapes. Scroll down the page if you need more explanations about the formulas, how to use them as well as worksheets. volume formulas



Volume of a Cube

A cube is a three-dimensional figure with six matching square sides.

cube

The figure above shows a cube. The dotted lines indicate edges hidden from your view.

If s is the length of one of its sides, then the volume of the cube is s × s × s

Volume of the cube = s3


How to find the volume of a cube?

The formula for the volume of a cube is s × s × s = s3, where s is the length of a side of the cube.


 

Volume of a Rectangular Solid

A rectangular solid is also called a rectangular prism or a cuboid.

In a rectangular solid, the length, width and height may be of different lengths.

rectangular solid

The volume of the above rectangular solid would be the product of the length, width and height that is

Volume of rectangular solid = lwh


How to find the volume of a rectangular prism or cuboid?

The formula for the volume of a cuboid is l × w × h = lwh, where l is the length, w is the width and h is the height of the rectangular prism. This video will give two examples of finding the volume of a rectangular prism.

Volume of a Prism

A prism is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. The other faces are in the shape of rectangles. They are called lateral faces.A prism is named after the shape of its base.

triangular prism and cuboid

When we cut a prism parallel to the base, we get a cross section of a prism. The cross section has the same size and shape as the base.

cut a triangular prism



The volume of a right prism is given by the formula:
Volume of prism = Area of base × length

V = Al

where A is the area of the base and l is the length or height of the prism.


How to find the volume of a triangular prism?

This video shows how to determine which is the base and the height of the triangular prism.


Volume of a Cylinder

A cylinder is a solid that has two parallel faces which are congruent circles. These faces form the bases of the cylinder. The cylinder has one curved surface. The height of the cylinder is the perpendicular distance between the two bases.

The volume of a cylinder is given by the formula:
Volume = Area of base × height

V = π r2h

where r = radius of cylinder and h is the height or length of cylinder.


How to find the volume of a cylinder, given that the radius is 9 and the height is 12.

Volume of a hollow cylinder

Sometimes you may be required to calculate the volume of a hollow cylinder or tube.

volume of hollow cylinder

Volume of hollow cylinder


where R is the radius of the outer surface and r is the radius of the inner surface.

Volume of hollow containers - cylinder and cone
How you can find the volume of a hollow cylinder and a cone using the formula of volume of prism and pyramid


 

Volume of a Cone

A cone is a solid with a circular base. It has a curved surface which tapers (i.e. decreases in size) to a vertex at the top. The height of the cone is the perpendicular distance from the base to the vertex.



The volume of a cone is given by the formula:

Volume of cone = Area of base × height

V = where r is the radius of the base and h is the height of the prism.


How to find the volume of a cone, given that the radius is 12 and the height is 16?

Volume of a Pyramid

A pyramid is a solid with a polygonal base and several triangular lateral faces. The lateral faces meet at a common vertex. The height of the pyramid is the perpendicular distance from the base to the vertex. The pyramid is named after the shape of its base. For example a rectangular pyramid or a triangular pyramid.

The volume of a pyramid is given by the formula:

Volume of pyramid = Area of base × height

V = where A is the area of the base and h is the height of the pyramid.


How to find the volume of a pyramid?

Make sure that you use the vertical height to substitute into the formula and not the slant height.


Volume of a Sphere

A sphere is a solid in which all the points on the round surface are equidistant from a fixed point, known as the center of the sphere. The distance from the center to the surface is the radius.


Volume of sphere = where r is the radius.


How to find the volume of a sphere? What is the volume of air in the ball?

Volume of a hemisphere


A hemisphere is half a sphere, with one flat circular face and one bowl-shaped face.

Volume of hemisphere where r is the radius


How to find the volume of a hemisphere? What is the volume of water in a bowl?


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


OML Search


We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.


[?] Subscribe To This Site

XML RSS
follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines