To determine the volume of the pyramid, we first need to find the dimensions of the cube, as the volume of the cube is given as 27 cubic inches.
The volume \( V \) of a cube is given by the formula:
\[ V = s^3 \]
where \( s \) is the length of a side of the cube. Given that the volume is 27 cubic inches, we can find \( s \) by solving:
\[ s^3 = 27 \]
Taking the cube root of both sides, we find:
\[ s = \sqrt[3]{27} = 3 \text{ inches} \]
Since the cube has a height of \( s = 3 \) inches, the height of the pyramid is also \( 3 \) inches, as given in the problem.
Next, we need to find the base area of the cube. The base area \( A \) of the cube can be calculated using:
\[ A = s^2 = 3^2 = 9 \text{ square inches} \]
The base area of the pyramid is the same as that of the cube, which is \( 9 \) square inches.
Now, we can calculate the volume of the pyramid using the formula for the volume \( V \) of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Here, the base area is \( 9 \) square inches and the height is \( 3 \) inches:
\[ V = \frac{1}{3} \times 9 \times 3 \] \[ V = \frac{27}{3} = 9 \text{ cubic inches} \]
Thus, the volume of the pyramid is 9 cubic inches.
The correct response is:
9 cubic inches.