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?(1 point)Responses288 cm3288 cm cubed1,728 cm31,728 cm cubed12 cm312 cm cubed576 cm3
Answers
GPT-4o mini
To find the volume of a square-based pyramid, we can use the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the base area of the pyramid is \( 144 \, \text{cm}^2 \) and the height is \( 12 \, \text{cm} \), we can substitute the values into the formula:
\[
V = \frac{1}{3} \times 144 \, \text{cm}^2 \times 12 \, \text{cm}
\]
First, we calculate the area multiplied by the height:
\[
144 \times 12 = 1728 \, \text{cm}^3
\]
Now we can calculate the volume:
\[
V = \frac{1}{3} \times 1728 \, \text{cm}^3 = 576 \, \text{cm}^3
\]
Thus, the volume of the pyramid is:
\[
\boxed{576 \, \text{cm}^3}
\]
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the base area of the pyramid is \( 144 \, \text{cm}^2 \) and the height is \( 12 \, \text{cm} \), we can substitute the values into the formula:
\[
V = \frac{1}{3} \times 144 \, \text{cm}^2 \times 12 \, \text{cm}
\]
First, we calculate the area multiplied by the height:
\[
144 \times 12 = 1728 \, \text{cm}^3
\]
Now we can calculate the volume:
\[
V = \frac{1}{3} \times 1728 \, \text{cm}^3 = 576 \, \text{cm}^3
\]
Thus, the volume of the pyramid is:
\[
\boxed{576 \, \text{cm}^3}
\]