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

### Volume of a Cube

#### How to find the volume of a cube?

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

### Volume of a Rectangular Solid

#### 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.

Examples:

1. Find the volume of a rectangular prism with sides 25 feet, 10 feet and 14 feet.

2. Find the volume of a rectangular prism with sides 5.4 inches, 7.5 inches and 18.3 inches.

### Volume of a 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.

Examples:

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

Volume = (area of base) × height

### Volume of a Cylinder

Volume = Area of base × height

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

Example:

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

### Volume of a hollow cylinder

**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?

Example:

1. Given a pipe with length = 12cm, outer diameter = 2m and thickness = 40cm. Calculate the amount of concrete used?

2. 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.

### Volume of a Cone

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

Example:

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

### Volume of a 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.

Example:

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

### Volume of a Sphere

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

Example:

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

### Volume of a hemisphere

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

Example:

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

You can use the free Mathway calculator and problem solver 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.

- 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.

More Geometry Lessons

Volume Games

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 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 = *s*^{3}

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

Examples:

1. Find the volume of a rectangular prism with sides 25 feet, 10 feet and 14 feet.

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

Examples:

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.

Volume = Area of base × height

V = π

r^{2}h

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

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

Example:

1. Given a pipe with length = 12cm, outer diameter = 2m and thickness = 40cm. Calculate the amount of concrete used?

2. 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 = Area of base × height

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

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 = Area of base × height

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

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** = where *r* is
the radius.

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

Example:

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

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 calculator and problem solver 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.

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