Question
A rectangular pyramid has a base area of 16 in.2, and a congruent rectangular prism has a volume of 288 in.3. What is the height of the rectangular pyramid?(1 point)Responses54 in.54 in.18 in.18 in.6 in.6 in.96 in.
Answers
GPT-4o mini
To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the base area of the pyramid is 16 in², we can set up the equation:
\[
V = \frac{1}{3} \times 16 \times h
\]
We need to find the height \(h\) of the pyramid. The volume of the pyramid is given as:
\[
V = 288 \, \text{in}^3
\]
Now we can equate the two expressions for volume:
\[
288 = \frac{1}{3} \times 16 \times h
\]
To solve for \(h\), first multiply both sides by 3 to eliminate the fraction:
\[
3 \times 288 = 16 \times h
\]
\[
864 = 16h
\]
Now, divide both sides by 16:
\[
h = \frac{864}{16}
\]
\[
h = 54
\]
Thus, the height of the rectangular pyramid is \(54\) inches.
The correct answer is \(54\) in.
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the base area of the pyramid is 16 in², we can set up the equation:
\[
V = \frac{1}{3} \times 16 \times h
\]
We need to find the height \(h\) of the pyramid. The volume of the pyramid is given as:
\[
V = 288 \, \text{in}^3
\]
Now we can equate the two expressions for volume:
\[
288 = \frac{1}{3} \times 16 \times h
\]
To solve for \(h\), first multiply both sides by 3 to eliminate the fraction:
\[
3 \times 288 = 16 \times h
\]
\[
864 = 16h
\]
Now, divide both sides by 16:
\[
h = \frac{864}{16}
\]
\[
h = 54
\]
Thus, the height of the rectangular pyramid is \(54\) inches.
The correct answer is \(54\) in.