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) Responses 12 cm3 12 cm cubed 576 cm3 576 cm cubed 1,728 cm3 1,728 cm cubed 288 cm3 288 cm cubed

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

Substituting the values into the formula:

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

Calculating the volume:

\[
\text{Volume} = \frac{1}{3} \times 144 \times 12
\]

First, calculate \(144 \times 12\):

\[
144 \times 12 = 1728
\]

Now, divide by 3:

\[
\text{Volume} = \frac{1728}{3} = 576 \, \text{cm}^3
\]

Thus, the volume of the square-based pyramid is \(576\) cubic centimeters.

The responses to choose from are:
- 12 cm³
- 576 cm³
- 1,728 cm³
- 288 cm³

The correct answer is \(576 \, \text{cm}^3\) or \(576 \, \text{cm cubed}\).