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

1,728 cm3
1,728 cm cubed

576 cm3
576 cm cubed

12 cm3
12 cm cubed

288 cm3

1 answer

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

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

Given that the base area is 144 square centimeters and the height is 12 centimeters, we can plug these values into the formula:

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

Calculating this step by step:

  1. First, multiply the base area by the height: \[ 144 \times 12 = 1,728 , \text{cm}^3 \]

  2. Now, take one third of that result: \[ \text{Volume} = \frac{1}{3} \times 1,728 = 576 , \text{cm}^3 \]

Therefore, the volume of the square-based pyramid is 576 cm³.