Question

How many cubic inches does the rectangular pyramid described below contain? Round answer to the nearest whole number please.
Measurements
Height 12 inch
Base length 14 inch
width 6 inch
Sides 13.89 inch.

Answer choices:
A. 1,167 in. squared
B. 389 in. squared
C. 1,008 in. squared
D. 336 in. squared

Answer 1

To find the volume of a rectangular pyramid, we can use the formula:

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

First, we need to calculate the area of the base. In this case, the base is rectangular, and its area can be calculated as:

\[
\text{Base Area} = \text{length} \times \text{width} = 14 \, \text{in.} \times 6 \, \text{in.} = 84 \, \text{in.}^2
\]

Next, we have the height of the pyramid, which is given as 12 inches. Now, we can substitute the base area and height into the volume formula:

\[
V = \frac{1}{3} \times 84 \, \text{in.}^2 \times 12 \, \text{in.}
\]

Calculating this step-by-step:

1. Multiply the base area by the height:
\[
84 \times 12 = 1,008 \, \text{in.}^3
\]

2. Now, divide by 3:
\[
V = \frac{1,008}{3} = 336 \, \text{in.}^3
\]

Thus, the volume of the rectangular pyramid is approximately \( 336 \, \text{in.}^3 \).

The answer is \( \text{D. } 336 \, \text{in.}^3 \).