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

Answer:

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.

Step-by-step 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 = $\sqrt{80}$=$4\sqrt{5}$

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.

Answer 2

The prism is a cube and the length of a side of the base is 20 centimeters.

Volume

Volume is the amount of space occupied by a closed container.

Let l be the length of the square base and h represent the height. Hence:

Volume of prism = length² * height

800 = l²(20)

l² = 400

l = 20 cm

Since the length of the base is the same as the height, the prism is a cube.

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