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

Answer:

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.

Step-by-step 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

$V=length \times breadth \times height$

Volume of prism is

$V=a \times a \times 20$

$V=20a^2$

Volume of prism is 800.

$800=20a^2$

Divide both sides by 20.

$40=a^2$           .... (1)

Taking square root both sides.

$\sqrt{40}=a$

The length of a side of the base is $\sqrt{40}$ 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.

$A=80(\sqrt{40})\approx 505.96$

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

The area of a lateral side is

$A=ha=20\times \sqrt{40}\approx 126.5$

Diagonals of base: Using Pythagoras we get

$hypotenuse=\sqrt{leg_1^2+leg_2^2}$

$d=\sqrt{a^2+a^2}$

$d=\sqrt{40+40}$

$d=\sqrt{80}$

Answer 2

Answer:

The area of the base is 40 cm^2.

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

Step-by-step 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.