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)
576 cm3
288 cm3
12 cm3
1, 728 cm

Answer 1

To find the volume of a square-based pyramid, we can use the formula:

\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

Given:

- Base Area = 144 square centimeters
- Height = 12 centimeters

Plugging in the values:

\[
\text{Volume} = \frac{1}{3} \times 144 \, \text{cm}^2 \times 12 \, \text{cm}
\]

Calculating step-by-step:

1. Multiply the base area by the height:
\[
144 \times 12 = 1728 \, \text{cm}^3
\]

2. Now, divide by 3:
\[
\frac{1728}{3} = 576 \, \text{cm}^3
\]

So, the volume of the square-based pyramid is:

\[
\boxed{576 \, \text{cm}^3}
\]