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More Geometry Lessons

Volume Games

In these lessons, we give:

1. 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**.

2. A more detailed explanation (examples and solutions) of each volume formula.

More Geometry Lessons

Volume Games

In these lessons, we give:

1. A table of volume formulas and surface area formulas used to calculate the volume and surface area of three-dimensional geometrical shapes:

2. A more detailed explanation (examples and solutions) of each volume formula.

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.

Explanations for the Surface Area Formulas

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 on the volume and surface area of cubes

More examples about the volume of cubes

More examples about the surface area of cubes

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 on volume and surface area of cuboids

More examples about the volume of cuboids

More examples about the surface area of cuboids

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.

Worksheets on surface area & volume of prisms & pyramids

More examples about the volume of prisms

More examples about the surface area of prisms

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.

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

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 = 1/3 × Area of base × height

V = 1/3 πr^{2}h where *r* is the radius of the base and *h*
is the height of the prism.

Worksheets to calculate volume of cones

More examples about the volume of cones

More examples about the surface area of cones

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 *h* is the height of the pyramid.

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

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.

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

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

Example:

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

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