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

133.33 dm3
133.33 dm cubed

447.2 dm3
447.2 dm cubed

149.07 dm3

1 answer

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

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

Given:

  • Length of the base (l) = 10 dm
  • Width of the base (w) = 4 dm
  • Height of the pyramid (h) = 10 dm

First, calculate the base area:

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

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

\[ V = \frac{1}{3} \times 40 , \text{dm}^2 \times 10 , \text{dm} \] \[ V = \frac{1}{3} \times 400 , \text{dm}^3 \] \[ V = \frac{400}{3} , \text{dm}^3 \approx 133.33 , \text{dm}^3 \]

Rounded to the nearest hundredth, the volume of the pyramid is:

133.33 dm³.