Question

name:
period: 1st 2nd 3rd 4th 5th 6th 7th 8th

• a pyramid and prism both have a base area of 56 and a height of 7. find the volume of the two figures and compare them.

prism	pramid	compared

Explanation:

Step1: Calculate volume of prism

The formula for the volume of a prism is \( V_{prism} = B \times h \), where \( B \) is the base area and \( h \) is the height. Given \( B = 56 \) and \( h = 7 \), we substitute these values:
\( V_{prism} = 56 \times 7 = 392 \)

Step2: Calculate volume of pyramid

The formula for the volume of a pyramid is \( V_{pyramid} = \frac{1}{3} \times B \times h \). Using \( B = 56 \) and \( h = 7 \):
\( V_{pyramid} = \frac{1}{3} \times 56 \times 7 = \frac{392}{3} \approx 130.67 \)

Step3: Compare the volumes

The volume of the prism is 392, and the volume of the pyramid is \( \frac{392}{3} \). The volume of the prism is three times the volume of the pyramid (since \( 392 = 3 \times \frac{392}{3} \)).

Answer:

• Prism Volume: \( 392 \)
• Pyramid Volume: \( \frac{392}{3} \) (or approximately \( 130.67 \))
• Comparison: The volume of the prism is three times the volume of the pyramid with the same base area and height.