A right rectangular pyramid has an altitude of 35 m, a length of 26 m, and a width of 31 m. What is the volume of the pyramid in m3

?(1 point)
Responses

84,630 m3
84,630 m cubed

28,210 m3
28,210 m cubed

9,403.33 m3
9,403.33 m cubed

30.67 m3

1 answer

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

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

Where the base area of a rectangular base is calculated as:

\[ \text{Base Area} = \text{Length} \times \text{Width} \]

In this case:

  • Length = 26 m
  • Width = 31 m
  • Height = 35 m

First, we calculate the base area:

\[ \text{Base Area} = 26 , \text{m} \times 31 , \text{m} = 806 , \text{m}^2 \]

Next, we can calculate the volume:

\[ \text{Volume} = \frac{1}{3} \times 806 , \text{m}^2 \times 35 , \text{m} \] \[ \text{Volume} = \frac{1}{3} \times 28110 , \text{m}^3 \] \[ \text{Volume} = 9370 , \text{m}^3 \]

So the volume of the pyramid is approximately:

\[ 9370 , \text{m}^3 \]

However, let's double-check this calculation:

\[ 806 \times 35 = 28210 \quad \text{(not 28110)} \] Now for the exact volume: \[ \text{Volume} = \frac{1}{3} \times 28210 , \text{m}^3 \approx 9403.33 , \text{m}^3 \]

Thus, the volume of the pyramid is approximately 9,403.33 m³.

The correct response is:

9,403.33 m³ (or 9,403.33 m cubed)