Question
Lena is looking for a new tent to go camping. She wants one with a volume of at least 200 cubic feet. The tent she is considering is 8 feet tall with a base of 8 feet by 8 feet. Will this tent have a large enough volume? Responses No, the volume is only 170.67 ft3 . No, the volume is only 170.67 feet cubed . Yes, the volume is 512 ft3 . Yes, the volume is 512 ft cubed . Yes, the volume is 1,536 ft3 . Yes, the volume is 1,536 ft cubed . No, the volume is only 24 ft3 .
Answers
GPT-4o mini
To determine the volume of the tent, we can use the formula for the volume of a rectangular prism (which is the shape of the tent):
\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]
The base of the tent is an 8 feet by 8 feet square:
\[
\text{Base Area} = 8 \, \text{feet} \times 8 \, \text{feet} = 64 \, \text{square feet}
\]
The height of the tent is 8 feet. Therefore, the volume is:
\[
\text{Volume} = 64 \, \text{sq ft} \times 8 \, \text{feet} = 512 \, \text{cubic feet}
\]
Since 512 cubic feet is greater than 200 cubic feet, the answer is:
**Yes, the volume is 512 ft³.**
\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]
The base of the tent is an 8 feet by 8 feet square:
\[
\text{Base Area} = 8 \, \text{feet} \times 8 \, \text{feet} = 64 \, \text{square feet}
\]
The height of the tent is 8 feet. Therefore, the volume is:
\[
\text{Volume} = 64 \, \text{sq ft} \times 8 \, \text{feet} = 512 \, \text{cubic feet}
\]
Since 512 cubic feet is greater than 200 cubic feet, the answer is:
**Yes, the volume is 512 ft³.**