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 28,210 m3 28,210 m cubed 9,403.33 m3 9,403.33 m cubed 84,630 m3 84,630 m cubed 30.67 m3 30.67 m cubed Skip to navigation page 14 of 14

1 answer

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

\[ V = \frac{1}{3} \cdot B \cdot h \]

where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height (altitude) of the pyramid.

For a right rectangular pyramid, the base area \( B \) can be calculated as:

\[ B = \text{length} \times \text{width} \]

In this case:

  • Length = 26 m
  • Width = 31 m
  • Height (altitude) = 35 m

First, we calculate the area of the base:

\[ B = 26,m \times 31,m = 806,m^2 \]

Next, we substitute \( B \) and \( h \) back into the volume formula:

\[ V = \frac{1}{3} \cdot 806,m^2 \cdot 35,m \]

Calculating this step by step:

\[ V = \frac{1}{3} \cdot 806 \cdot 35 \]

Calculating \( 806 \cdot 35 \):

\[ 806 \cdot 35 = 28110 \]

Now, divide by 3:

\[ V = \frac{28110}{3} = 9370 \]

Thus, the volume of the pyramid is:

\[ V \approx 9370,m^3 \]

Looking at the provided options, the closest volume is:

9,403.33 m³

Therefore, the correct response is 9,403.33 m cubed.