Question

A right rectangular prism with square bases has a height of 20 centimeters and a volume of 800 cubic centimeters. Which statements describe the prism? Check all that apply.

1. The prism is a cube.
2, The diagonal of the base is 4 radical 5 centimeters.
3. The length of a side of the base is 20 centimeters.
4. The area of a base is 40 square centimeters.
5. The area of a lateral side between the bases is about 126.5 square centimeters.

Answer 1

The diagonal of the base is 4√5 centimeters.

The area of a base is 40 square centimeters.

The area of a lateral side between the bases is about 126.5 square centimeters.

Explanation:

The volume of any rectangular prism can be found by the formula

volume =B.h

where B = area of base and h is the height of the prism.

It is given the volume of prism is 800 cubic centimeters and height is 20 centimeters.

Substituting these values in the volume formula :

800= B(20)

Or B= 800÷20=40.

Hence area of base is 40 square centimeters.

The diagonal of base =
`√(80)`=
`4√(5)`

The Volume of prism is 800 cubic unit and base area is 40 square units .Lateral area = area of all sides except the base = 126.5 square centimeters.