5
QuizMultiple Choice

Volume of Prisms — Quiz

Question 5 • MASTER COURSE Geometry

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? Choose three correct answers.

Answer
A
The area of a base is 40 square centimeters.
B
The area of a lateral side between the bases is about 126 point 5 square centimeters.
C
The diagonal of the base is 4 square root of 5 centimeters.
D
The length of a side of the base is 20 centimeters.
E
The prism is a cube.

Explanation

The base area is volume divided by height: 800 ÷ 20 = 40 square centimeters, so B is correct. Since the base is square, each side is √40 = 2√10 centimeters; the prism is not a cube, and the side is not 20 centimeters. A lateral side has area 20 × √40 = 40√10 ≈ 126.5 square centimeters, so C is correct. The base diagonal is √(40 + 40) = √80 = 4√5 centimeters, so E is correct.

AI-written and checked against the verified answer.

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