What is the volume of the rectangular pyramid described below?

Measurements
Width 12 m
Base length 12 m
Height 10 m
Slanted sides 11.66 m

Answer choices
A. 480 m squared
B. 1,440 m squared
C. 144 m squared
D. 559.68 m squared

1 answer

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

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

For the given pyramid:

  • The base is a rectangle with a width of \(12 , \text{m}\) and a length of \(12 , \text{m}\).
  • The height of the pyramid is \(10 , \text{m}\).

First, we calculate the base area:

\[ \text{Base Area} = \text{Width} \times \text{Base Length} = 12 , \text{m} \times 12 , \text{m} = 144 , \text{m}^2 \]

Now we can substitute the base area and height into the volume formula:

\[ \text{Volume} = \frac{1}{3} \times 144 , \text{m}^2 \times 10 , \text{m} \]

Calculating this gives:

\[ \text{Volume} = \frac{1}{3} \times 1440 , \text{m}^3 = 480 , \text{m}^3 \]

Thus, the volume of the rectangular pyramid is

\(\boxed{480 , \text{m}^3}\).

The correct answer choice is A. 480 m³.