To find the volume of the pyramid, we can use the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
From the problem, we know:
- The base area of the pyramid is \( 36 \) square inches.
- The height of the pyramid is \( 6 \) inches.
Now, we can substitute these values into the volume formula:
\[ V = \frac{1}{3} \times 36 \times 6 \]
First, calculate \( 36 \times 6 \):
\[ 36 \times 6 = 216 \]
Now substitute this back into the volume formula:
\[ V = \frac{1}{3} \times 216 \]
Now divide \( 216 \) by \( 3 \):
\[ V = 72 \]
Thus, the volume of the pyramid is:
\[ \boxed{72} \text{ cubic inches} \]
To confirm consistency, let's also check the given information about the cube. The volume of a cube is given by \( V = \text{side}^3 \). We are given the volume of the cube as \( 216 \) cubic inches. To find the side length, we solve:
\[ \text{side}^3 = 216 \]
Taking the cube root, we get:
\[ \text{side} = \sqrt[3]{216} = 6 \]
With the side length being \( 6 \) inches, the height and base consideration fits in as well, confirming that both shapes share the same dimensions, with the pyramid having a volume of \( \boxed{72} \text{ cubic inches} \).
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