Use the image to answer the question.

An illustration shows a rectangular pyramid with a length of 10 decimeters, a width of 4 decimeters, a perpendicular height of 10 decimeters, and a slant height of 11.18 decimeters. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.

What is the volume of the pyramid? Round to the nearest hundredth.

(1 point)
Responses

400 dm3
400 dm cubed

149.07 dm3
149.07 dm cubed

133.33 dm3
133.33 dm cubed

447.2 dm3

1 answer

The volume \( V \) of a rectangular pyramid can be calculated using the formula:

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

For this pyramid:

  • The base dimensions are given as length \( l = 10 \) dm and width \( w = 4 \) dm.
  • The height \( h = 10 \) dm.

First, calculate the area of the base:

\[ \text{Base Area} = l \times w = 10 , \text{dm} \times 4 , \text{dm} = 40 , \text{dm}^2 \]

Now, substitute the base area and height into the volume formula:

\[ V = \frac{1}{3} \times 40 , \text{dm}^2 \times 10 , \text{dm} \]

Calculating this:

\[ V = \frac{1}{3} \times 400 , \text{dm}^3 = \frac{400}{3} , \text{dm}^3 \approx 133.33 , \text{dm}^3 \]

Thus, the volume of the pyramid is approximately \( 133.33 , \text{dm}^3 \).

So the correct response is:

133.33 dm cubed.