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? Select three options. The prism is a cube. The diagonal of the base is 4 centimeters. The length of a side of the base is 20 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.

Answer 1

b d e

Explanation:

Answer 2

The diagonal of the base is 4 radical 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:

step 1

Find the area of the base of the rectangular prism

The volume of the prism is equal to

`V=Bh`

where

B is the area of the square base

h is the height of prism

we have

`V=800\ cm^3`

`h=20\ cm`

substitute and solve for B

`800=B(20)`

`B=800/(20)`

`B=40\ cm^2`

step 2

Find the length side of the square base b

`b=√(B)\ cm` -----> is a square base

substitute the value of B

`b=√(40)\ cm`

`b=2√(10)\ cm`

step 3

Find the diagonal of the base

Applying the Pythagoras theorem

`d=\sqrt{√(40)^2+√(40)^2}`

`d=√(80)\ cm`

`d=4√(5)\ cm`

step 4

Find the area of a lateral side between the bases

The area of a lateral side is

`A=bh`

substitute

`A=2√(10)(20)`

`A=126.49\ cm^2`

Verify each statement

case 1) The prism is a cube

The statement is false, because the cube has three equal length sides, and the rectangular prism has not three equal length sides

case 2) The diagonal of the base is 4 radical 5 centimeters

The statement is true (see the step 3)

case 3) The length of a side of the base is 20 centimeters

The statement is false, because the length of the base is
`2√(10)\ cm`

case 4) The area of a base is 40 square centimeters

The statement is true (see the step 1)

case 5) The area of a lateral side between the bases is about 126.5 square centimeters

The statement is true (see the step 4)