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

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

  2. Now, divide by 3: \[ \text{Volume} = \frac{1}{3} \times 1728 , \text{cm}^3 = 576 , \text{cm}^3 \]

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

The correct response is 576 cm cubed.