To solve the problem of finding the volume of the pyramid, we need to follow these steps:
1. Calculate the area of the base of the pyramid (B):
The base of the pyramid is rectangular in shape, so we use the formula for the area of a rectangle:
[tex]\[
B = \text{length} \times \text{width}
\][/tex]
Given:
[tex]\[
\text{length} = 9 \, \text{m}
\][/tex]
[tex]\[
\text{width} = 8 \, \text{m}
\][/tex]
Plugging these values into the formula, we get:
[tex]\[
B = 9 \, \text{m} \times 8 \, \text{m} = 72 \, \text{m}^2
\][/tex]
2. Calculate the volume of the pyramid (V):
Now, we use the formula for the volume of a pyramid:
[tex]\[
V = \frac{1}{3} B h
\][/tex]
Given:
[tex]\[
h = 12 \, \text{m}
\][/tex]
[tex]\[
B = 72 \, \text{m}^2
\][/tex]
Plugging in these values, we get:
[tex]\[
V = \frac{1}{3} \times 72 \, \text{m}^2 \times 12 \, \text{m}
\][/tex]
Simplifying this, we find:
[tex]\[
V = \frac{1}{3} \times 864 \, \text{m}^3 = 288 \, \text{m}^3
\][/tex]
Therefore, the volume of the pyramid is:
[tex]\[
288 \, \text{m}^3
\][/tex]
So, the correct answer is:
C. [tex]\( 288 \, \text{m}^3 \)[/tex]
