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?
What is the volume of the pyramid?
Answers
GPT-4o mini
To find the volume \( V \) of a pyramid, we can use the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, the base is a rectangle. The area \( A \) of the rectangular base can be calculated as:
\[
A = \text{length} \times \text{width}
\]
Given that the base length is 10 centimeters and the width is 7 centimeters, we can find the area:
\[
A = 10 \, \text{cm} \times 7 \, \text{cm} = 70 \, \text{cm}^2
\]
The height of the pyramid is given as 11 centimeters. We can now calculate the volume:
\[
V = \frac{1}{3} \times 70 \, \text{cm}^2 \times 11 \, \text{cm}
\]
Calculating this step-by-step:
1. Calculate the product of the base area and height:
\[
70 \, \text{cm}^2 \times 11 \, \text{cm} = 770 \, \text{cm}^3
\]
2. Calculate the volume:
\[
V = \frac{1}{3} \times 770 \, \text{cm}^3 = \frac{770}{3} \, \text{cm}^3 \approx 256.67 \, \text{cm}^3
\]
Therefore, the volume of the pyramid is
\[
\boxed{256.67 \, \text{cm}^3}
\]
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, the base is a rectangle. The area \( A \) of the rectangular base can be calculated as:
\[
A = \text{length} \times \text{width}
\]
Given that the base length is 10 centimeters and the width is 7 centimeters, we can find the area:
\[
A = 10 \, \text{cm} \times 7 \, \text{cm} = 70 \, \text{cm}^2
\]
The height of the pyramid is given as 11 centimeters. We can now calculate the volume:
\[
V = \frac{1}{3} \times 70 \, \text{cm}^2 \times 11 \, \text{cm}
\]
Calculating this step-by-step:
1. Calculate the product of the base area and height:
\[
70 \, \text{cm}^2 \times 11 \, \text{cm} = 770 \, \text{cm}^3
\]
2. Calculate the volume:
\[
V = \frac{1}{3} \times 770 \, \text{cm}^3 = \frac{770}{3} \, \text{cm}^3 \approx 256.67 \, \text{cm}^3
\]
Therefore, the volume of the pyramid is
\[
\boxed{256.67 \, \text{cm}^3}
\]