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)

• 288 cm?
O 12 cm?
О 1, 728 ст3
О 576 ст3

1 answer

The volume \( V \) of a square-based pyramid can be calculated using the formula:

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

In this case, the base area is given as \( 144 , \text{cm}^2 \) and the height is given as \( 12 , \text{cm} \). Plugging these values into the formula, we get:

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

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

\[ 144 \times 12 = 1728 , \text{cm}^3 \]

Now, divide by 3:

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

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

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