Question

A rectangular pyramid has a length of 7 cm and a width of 9 cm. Its volume is 231 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid. Show all your work.

(2 points)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The formula for the volume of a rectangular pyramid is given by:

\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]

Given that the length is 7 cm and the width is 9 cm, the base area of the pyramid can be calculated as:
\[ \text{base area} = 7 \times 9 = 63 \, \text{cm}^2 \]

Plugging in the values for the volume and base area into the formula, we have:
\[ 231 = \frac{1}{3} \times 63 \times \text{height} \]

Solving for the height:
\[ \text{height} = \frac{231}{\frac{1}{3} \times 63} \]
\[ \text{height} = \frac{231}{21} \]
\[ \text{height} = 11 \, \text{cm} \]

Therefore, the height of the rectangular pyramid is 11 cm.

Answer 2

can you say it all again, those brackets r confusing

Answer 3

[AI-generated answer — Bot GPT 3.5]

Absolutely! Let's break it down step by step without using brackets:

Given:
Length = 7 cm
Width = 9 cm
Volume = 231 cubic centimeters

The formula for the volume of a rectangular pyramid is:
Volume = (1/3) * base area * height

Find the base area:
Base area = Length * Width
Base area = 7 cm * 9 cm
Base area = 63 square cm

Using the volume and base area in the formula:
231 = (1/3) * 63 * height

Solving for the height:
231 = 21 * height
height = 231 / 21
height = 11 cm

Therefore, the height of the rectangular pyramid is 11 cm.