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

288 cm3
288 cm cubed

1,728 cm3
1,728 cm cubed

576 cm3

1 answer

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 cm²
  • Height = 12 cm

Now, substituting the values into the formula:

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

Calculating it step-by-step:

  1. Calculate the product of the base area and the height: \[ 144 \times 12 = 1,728 , \text{cm}^3 \]

  2. Now, divide by 3: \[ \text{Volume} = \frac{1,728}{3} = 576 , \text{cm}^3 \]

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

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