In these lessons, we provide:

- 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 (examples and solutions) of each volume formula.

**Related Pages**

Volume Formulas Explained

Explanations For The Surface Area Formulas

More Geometry Lessons

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 volume formulas, examples on how to use the formulas and worksheets.

A cube is a three-dimensional figure with six matching square sides. The figure below shows a cube
with sides *s*.

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

Volume of the cube = *s*^{3}

**Worksheets and More Examples:**

Worksheets on the volume and surface area of cubes

More examples about the volume of cubes

More examples about the surface area of cubes

The formula for the volume of a cube is *s* × *s* × *s* = *s*^{3}, where *s* is the length of
a side of the cube.

**Example:**

Find the volume of a cube with sides = 4cm

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.

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

Volume of rectangular solid = *lwh*

**Worksheets And More Examples:**

Worksheets on volume and surface area of cuboids

More examples about the volume of cuboids

More examples about the surface area of cuboids

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.

**Examples:**

- Find the volume of a rectangular prism with sides 25 feet, 10 feet and 14 feet.
- Find the volume of a rectangular prism with sides 5.4 inches, 7.5 inches and 18.3 inches.

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.

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.

The volume of a right prism is given by the formula:

Volume of prism = Area of base × length

**V = Al**

where

**Worksheets and More Examples:**

Worksheets on surface area & volume of prisms & pyramids

More examples about the volume of prisms

More examples about the surface area of prisms

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

**Example:**

Find the value of a triangular prism, use the following formula:

Volume = (area of base) × height

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 r^{2}h **

where

**Worksheets and More Examples:**

Worksheets to calculate volume of cylinders

Worksheets to calculate surface area of cylinders

Worksheets on volume and surface area of cylinders

Worksheets on surface area of of cylinders and pipes

More examples about the volume of cylinders

More examples about the surface area of cylinders

**How to find the volume of a cylinder?**

**Example:**

Find the volume of a cylinder with radius 9 and height 12

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

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?

**Examples:**

- Given a pipe with length = 12cm, outer diameter = 2m and thickness = 40cm. Calculate the amount of concrete used?
- Given that an ice-cream cone has a diameter of 65mm, height of 15cm and thickness of 2mm. Calculate the volume of wafer in the 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 = 1/3 × Area of base × height

**V = 1/3 πr ^{2}h **

where

**Worksheets and More Examples:**

Worksheets to calculate volume of cones

More examples about the volume of cones

More examples about the surface area of cones

**How to find the volume of a cone?**

**Example:**

Find the volume of a cone with radius is 12ft and height is 16ft.

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 = 1/3 × Area of base × height

**V = 1/3 Ah where A **

is the area of the base and

**Worksheets and More Examples:**

Worksheet to calculate the volume of square pyramids

Worksheets on volume of prisms and pyramids

More examples about the volume of pyramids

More examples about the surface area of pyramids

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

**Example:**

Find the volume of a pyramid with sides = 9ft, vertical height = 5ft and slant height = 8ft.

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 = 4/3 πr^{3}

where *r* is the radius.

**How to find the volume of a sphere?**

**Example:**

Find the volume of air in the ball with radius = 3cm

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

Volume of hemisphere where *r* is the radius.

**Worksheets and More Examples:**

Worksheet to calculate the volume of spheres

Worksheets to calculate the surface area of spheres

More examples about the volume of spheres

More examples about the surface area of spheres

**How to find the volume of a hemisphere?**

**Example:**

Find the volume of water in a bowl with diameter = 33cm

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