Question

An illustration shows a 3 D pyramid with a rectangular base. The length, width, and height measurements are labeled. The sides on the front that are visible are shown as solid lines and the sides at the back are shown as dashed lines. The base length is labeled 10 centimeters and the width is labeled 7 centimeters. The height is shown as a dotted perpendicular line from the top vertex to the base and is labeled 11 centimeters. The dotted line continues to the base length to make a right angle.
What is the volume of the pyramid?

(1 point)
cm3

Answer 1

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

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

For a pyramid with a rectangular base, the base area can be calculated using:

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

Given the pyramid's dimensions:
- Length = 10 cm
- Width = 7 cm
- Height = 11 cm

First, calculate the base area:

\[
\text{Base Area} = 10 \, \text{cm} \times 7 \, \text{cm} = 70 \, \text{cm}^2
\]

Next, use the base area to calculate the volume:

\[
\text{Volume} = \frac{1}{3} \times 70 \, \text{cm}^2 \times 11 \, \text{cm}
\]

Calculating:

\[
\text{Volume} = \frac{1}{3} \times 770 \, \text{cm}^3 = \frac{770}{3} \, \text{cm}^3 \approx 256.67 \, \text{cm}^3
\]

Thus, the volume of the pyramid is approximately:

\[
\boxed{256.67} \, \text{cm}^3
\]