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)
• 288 cm?
O 12 cm?
О 1, 728 ст3
О 576 ст3
• 288 cm?
O 12 cm?
О 1, 728 ст3
О 576 ст3
Answers
GPT-4o mini
The volume \( V \) of a square-based pyramid can be calculated using the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, the base area is given as \( 144 \, \text{cm}^2 \) and the height is given as \( 12 \, \text{cm} \). Plugging these values into the formula, we get:
\[
V = \frac{1}{3} \times 144 \, \text{cm}^2 \times 12 \, \text{cm}
\]
First, calculate \( 144 \times 12 \):
\[
144 \times 12 = 1728 \, \text{cm}^3
\]
Now, divide by 3:
\[
V = \frac{1728 \, \text{cm}^3}{3} = 576 \, \text{cm}^3
\]
Thus, the volume of the square-based pyramid is:
\[
\boxed{576 \, \text{cm}^3}
\]
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, the base area is given as \( 144 \, \text{cm}^2 \) and the height is given as \( 12 \, \text{cm} \). Plugging these values into the formula, we get:
\[
V = \frac{1}{3} \times 144 \, \text{cm}^2 \times 12 \, \text{cm}
\]
First, calculate \( 144 \times 12 \):
\[
144 \times 12 = 1728 \, \text{cm}^3
\]
Now, divide by 3:
\[
V = \frac{1728 \, \text{cm}^3}{3} = 576 \, \text{cm}^3
\]
Thus, the volume of the square-based pyramid is:
\[
\boxed{576 \, \text{cm}^3}
\]