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 1,728 cm3 1,728 cm cubed 288 cm3 288 cm cubed 576 cm3
Answers
GPT-4o mini
To find the volume of a square-based pyramid, you can use the formula:
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, the base area is given as \(144 \, \text{cm}^2\) and the height is given as \(12 \, \text{cm}\).
Substituting the values into the formula:
\[
\text{Volume} = \frac{1}{3} \times 144 \times 12
\]
First, calculate \(144 \times 12\):
\[
144 \times 12 = 1728
\]
Now apply the fraction:
\[
\text{Volume} = \frac{1}{3} \times 1728 = \frac{1728}{3} = 576
\]
Thus, the volume of the square-based pyramid is:
\[
576 \, \text{cm}^3
\]
So the answer is \(576 \, \text{cm}^3\).
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, the base area is given as \(144 \, \text{cm}^2\) and the height is given as \(12 \, \text{cm}\).
Substituting the values into the formula:
\[
\text{Volume} = \frac{1}{3} \times 144 \times 12
\]
First, calculate \(144 \times 12\):
\[
144 \times 12 = 1728
\]
Now apply the fraction:
\[
\text{Volume} = \frac{1}{3} \times 1728 = \frac{1728}{3} = 576
\]
Thus, the volume of the square-based pyramid is:
\[
576 \, \text{cm}^3
\]
So the answer is \(576 \, \text{cm}^3\).