To solve this problem, let's use the formula for the volume of a pyramid. The volume [tex]\( V \)[/tex] of a pyramid is given by:
[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
Let's break it down step by step:
1. Identify the height and the base area of the pyramid:
- Height ([tex]\( h \)[/tex]): 10 inches
- Base area ([tex]\( A \)[/tex]): 21 square inches
2. Substitute the given values into the formula for the volume of a pyramid:
[tex]\[ V = \frac{1}{3} \times 21 \times 10 \][/tex]
3. Calculate the volume:
[tex]\[ V = \frac{1}{3} \times 210 \][/tex]
[tex]\[ V = 70 \text{ cubic inches} \][/tex]
Thus, the volume of the pyramid is [tex]\( 70 \)[/tex] cubic inches.
So, the correct answer is:
C. [tex]\( 70 \ i^3 \)[/tex]
