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

The area of the base is 40 cm^2.

The area of a lateral surface is 126.5 cm^2.

Explanation:

The area of the base = volume / height

= 800/20

= 40 cm^2.

The side length of the square base is √40 cms which means that the area of a lateral side is 20 * √40 = 126.5 cm^2.

Answer 2

The correct statements are:

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:

Given information: A right rectangular prism with square bases has Height = 20 cm and volume = 800 cubic cm.

Let a be the length of a side of the base.

Volume of a right rectangular prism is

`V=length * breadth * height`

Volume of prism is

`V=a * a * 20`

`V=20a^2`

Volume of prism is 800.

`800=20a^2`

Divide both sides by 20.

`40=a^2` .... (1)

Taking square root both sides.

`√(40)=a`

The length of a side of the base is
`√(40)` centimeters.

Area of square base is

`A=a^2`

Using (1) we get,

`A=40`

The area of a base is 40 square centimeters.

The area of a lateral side between the bases is

`A=2(l+b)h`

`A=2(a+a)(20)`

`A=40(2a)`

`A=80a`

Substitute the value of a.

`A=80(√(40))\approx 505.96`

Therefore the area of a lateral side between the bases is about 505.96 square centimeters.

The area of a lateral side is

`A=ha=20* √(40)\approx 126.5`

Diagonals of base: Using Pythagoras we get

`hypotenuse=√(leg_1^2+leg_2^2)`

`d=√(a^2+a^2)`

`d=√(40+40)`

`d=√(80)`