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. Make it short, simple and laconic

Answer 1

Make it shorter like no longer than 4 sentences

Answer 2

The volume \( V \) of a pyramid is given by the formula:

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

For a rectangular base, the base area \( A \) is calculated as:

\[
A = \text{Length} \times \text{Width} = 7 \, \text{cm} \times 9 \, \text{cm} = 63 \, \text{cm}^2
\]

Substituting the values into the volume formula:

\[
231 \, \text{cm}^3 = \frac{1}{3} \times 63 \, \text{cm}^2 \times h
\]

To isolate \( h \), first multiply both sides by 3:

\[
693 \, \text{cm}^3 = 63 \, \text{cm}^2 \times h
\]

Next, divide both sides by 63:

\[
h = \frac{693 \, \text{cm}^3}{63 \, \text{cm}^2} = 11 \, \text{cm}
\]

Thus, the height of the pyramid is

\[
\boxed{11 \, \text{cm}}
\]

Answer 3

The volume \( V \) of a pyramid is calculated as \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). The base area is \( 7 \, \text{cm} \times 9 \, \text{cm} = 63 \, \text{cm}^2 \). Setting the volume equation \( 231 = \frac{1}{3} \times 63 \times h \) leads to \( h = \frac{693}{63} = 11 \, \text{cm} \). Thus, the height of the pyramid is \( \boxed{11 \, \text{cm}} \).