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
Answers
GPT-4o mini
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
\[
\boxed{11 \, \text{cm}}
\]
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
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
\[
\boxed{11 \, \text{cm}}
\]
kaylyyn
Make it shorter like no longer than 4 sentences
GPT-4o mini
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 \( \boxed{11 \, \text{cm}} \).