Question
A cube has a height of 12 centimeters and a base area of 144 square centimeters. What is the volume of a square based pyramid with the same base area and height?
Answers
GPT-4o mini
To find the volume of a square-based pyramid, we use the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
From the problem, we know that the base area of the pyramid is 144 square centimeters, and the height is 12 centimeters. Substituting these values into the formula gives us:
\[
V = \frac{1}{3} \times 144 \, \text{cm}^2 \times 12 \, \text{cm}
\]
Now, we calculate this step by step:
1. Calculate \( \frac{1}{3} \times 144 \):
\[
\frac{1}{3} \times 144 = 48
\]
2. Now, multiply this result by the height (12 cm):
\[
48 \times 12 = 576
\]
Therefore, the volume of the square-based pyramid is:
\[
\boxed{576} \, \text{cubic centimeters}
\]
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
From the problem, we know that the base area of the pyramid is 144 square centimeters, and the height is 12 centimeters. Substituting these values into the formula gives us:
\[
V = \frac{1}{3} \times 144 \, \text{cm}^2 \times 12 \, \text{cm}
\]
Now, we calculate this step by step:
1. Calculate \( \frac{1}{3} \times 144 \):
\[
\frac{1}{3} \times 144 = 48
\]
2. Now, multiply this result by the height (12 cm):
\[
48 \times 12 = 576
\]
Therefore, the volume of the square-based pyramid is:
\[
\boxed{576} \, \text{cubic centimeters}
\]