Dahlia makes a square-based pyramid out of clay. It has a height of 6 inches and a base area of 36 square inches. Then, Dahlia makes a cube out of clay. The cube has the same height and the same base area as the pyramid. What is the volume of the pyramid in cubic inches if the volume of the cube is 216? Responses(1 point)

Question

Responses

648
648

216
216

144
144

72

Answer 1

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

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

Given that the base area of the pyramid is 36 square inches and the height is 6 inches, we can substitute these values into the formula:

\[ V = \frac{1}{3} \times 36 \times 6 \]

Calculating this step-by-step:

1. Calculate the volume without the \(\frac{1}{3}\): \[ 36 \times 6 = 216 \]

2. Now, multiply by \(\frac{1}{3}\): \[ V = \frac{1}{3} \times 216 = 72 \text{ cubic inches} \]

So, the volume of the pyramid is \( \boxed{72} \) cubic inches.