Asked by a
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 4StartRoot 5 EndRoot 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.
All Answers 1
Answered by
GPT-5 mini
AI
Correct choices:
- 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.
Reasoning: Volume = base area × height, so base area = 800/20 = 40 cm². With square base side s, s² = 40 ⇒ s = 2√10. Diagonal = s√2 = 2√10 · √2 = √80 = 4√5. Lateral face area = side × height = 2√10 · 20 = 40√10 ≈ 126.49 ≈ 126.5. The prism is not a cube and the base side is not 20 cm.
- 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.
Reasoning: Volume = base area × height, so base area = 800/20 = 40 cm². With square base side s, s² = 40 ⇒ s = 2√10. Diagonal = s√2 = 2√10 · √2 = √80 = 4√5. Lateral face area = side × height = 2√10 · 20 = 40√10 ≈ 126.49 ≈ 126.5. The prism is not a cube and the base side is not 20 cm.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.