Question
A square-based pyramid has a volume of 66 cubic units. If its height is 10 units, what is the area of the pyramid’s base?(1 point) Responses 198 square units 198 square units 2,200 square units 2,200 square units 22 square units 22 square units 19.8 square units
Answers
GPT-4o mini
The volume \( V \) of a square-based pyramid can be calculated using the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the volume \( V \) is 66 cubic units and the height \( h \) is 10 units, we can rearrange the formula to find the base area \( B \):
\[
66 = \frac{1}{3} \times B \times 10
\]
To isolate the base area \( B \), we first multiply both sides by 3:
\[
198 = B \times 10
\]
Now, divide both sides by 10:
\[
B = \frac{198}{10} = 19.8 \text{ square units}
\]
Thus, the area of the pyramid's base is **19.8 square units**.
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the volume \( V \) is 66 cubic units and the height \( h \) is 10 units, we can rearrange the formula to find the base area \( B \):
\[
66 = \frac{1}{3} \times B \times 10
\]
To isolate the base area \( B \), we first multiply both sides by 3:
\[
198 = B \times 10
\]
Now, divide both sides by 10:
\[
B = \frac{198}{10} = 19.8 \text{ square units}
\]
Thus, the area of the pyramid's base is **19.8 square units**.