Volume of rectangular prisms

# Volume formula intuition

Practice problems that help you see why the volume formula makes sense.

## Volume formula intuition

Problem 1

The rectangular prism has layers separated by color.

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

Each colored layer is made up of unit cubes.

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

**What is the volume of the rectangular prism?**

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

Explain

Problem 2

The rectangular prism has slices separated by color.

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

Each colored slice is made up of unit cubes.

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

**What is the volume of the rectangular prism?**

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

Explain

Problem 3

The rectangular prism has slices separated by color.

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

Each colored slice is made up of unit cubes.

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

**What is the volume of the rectangular prism?**

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

Explain

Problem 4

The rectangular prism has layers separated by color.

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

Each colored layer is made up of unit cubes.

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

**What is the volume of the rectangular prism?**

**Your answer should be**- an integer, like $6$6
- an
*exact*decimal, like $0.75$0, point, 75 - a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4

Explain

*Want to learn more about the volume formula? Check out this video.*