Perimeter, Area, Volume:

Introduction to Volume

To find the volume of an object we count how many unit cubes fit within the object. This is how we measure 3-D objects. The following video will explain what a unit cube is as well as showing how to find the volume of an object.

Video Source (05:27 mins) | Transcript

\(\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}\)

Volume is 3 dimensional because we are using 3 dimensions or directions multiplied together to find the volume.

Real World Application

Just as things to the power of 2 are “squared”, things to the power of 3 are “cubed.” The number \(4^{3}\) is pronounced “four to the power of 3” or “four to the third power” or “four cubed.”

Additional Resources

Khan Academy: Introduction to Volume (7:50 mins; Transcript)
Khan Academy: Volume with Unit Cubes (2:12 mins; Transcript)

Practice Problems

A wooden block has a length of 4 inches, a width of 4 inches, and a height of 4 inches. Find the volume of the wooden block.

A rectangular swimming pool has a length of 20 ft, a width of 12 ft, and a depth of 6 ft. Find the volume of the swimming pool.

A brick has a length of 20 cm, a width of 9 cm, and a height of 5 cm. Find the volume of the brick.

A cardboard moving box measures 16 in. long, 10 in. wide, and 12 in. high. Find the volume of the moving box.

A large rectangular fish tank is 3 m long and 1 m wide and has a height of 2 m. Find the volume of the fish tank.

A small rectangular juice box has a length of 60 mm, a width of 40 mm, and a height of 105 mm. Find the volume of the juice box.

Solutions

\(64\text{ in}^{3}\) (Solution Video | Transcript)
\(1440\text{ ft}^{3}\) (Written Solution)

The swimming pool is measured in feet.

When we find the volume of a rectangular solid, we need to find the number of unit cubes in the rectangular solid. In this case, we are measuring the volume in feet, so we want to find out how many 1 foot by 1 foot by 1 foot cubes it would take to fill the pool.

To find the volume of the pool, we multiply the length times the width times the height.

20 × 12 × 6 = 1440

So the volume of the swimming pool is 1440 \({\text{ft}}^{3}\)
\(900\text{ cm}^{3}\)
\(1920\text{ in}^{3}\) (Written Solution)

The moving box is measured in inches.

When we find the volume of a rectangular solid, we need to find out how many unit cubes would fit into the rectangular solid. Since we are measuring this box in inches, we need to find how many 1 inch by 1 inch by 1 inch cubes would fit into the box.

To find the volume of the box, we multiply the length times the width times the height.

16 × 10 × 12 = 1920

So the volume of the box is 1920 \({\text{in}}^{3}\)
\(6 \: {\text{m}}^{3}\)
\(252,000\text{ mm}^{3}\) (Solution Video | Transcript)