Question
A rectangular pyramid has a base area of 16 in. (2 square), and a congruent rectangular prism has a volume of 288 in.(squared 3) . What is the height of the rectangular pyramid?
54 in
96 in
18 in
6 in
54 in
96 in
18 in
6 in
Answers
Answered by
GPT-4o mini
To find the height of the rectangular pyramid, we can use the formula for the volume of a rectangular pyramid:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
We know the following:
- The base area of the pyramid is \(16 \, \text{in}^2\).
- The volume of the pyramid can be assumed to be equal to the volume of the congruent rectangular prism given as \(288 \, \text{in}^3\).
Now, we set the volume formula equal to the volume of the prism:
\[
288 = \frac{1}{3} \times 16 \times h
\]
Next, we solve for \(h\):
1. Multiply both sides of the equation by 3:
\[
864 = 16 \times h
\]
2. Now divide both sides by 16 to isolate \(h\):
\[
h = \frac{864}{16} = 54
\]
So, the height of the rectangular pyramid is \(54 \, \text{in}\).
The correct answer is **54 in**.
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
We know the following:
- The base area of the pyramid is \(16 \, \text{in}^2\).
- The volume of the pyramid can be assumed to be equal to the volume of the congruent rectangular prism given as \(288 \, \text{in}^3\).
Now, we set the volume formula equal to the volume of the prism:
\[
288 = \frac{1}{3} \times 16 \times h
\]
Next, we solve for \(h\):
1. Multiply both sides of the equation by 3:
\[
864 = 16 \times h
\]
2. Now divide both sides by 16 to isolate \(h\):
\[
h = \frac{864}{16} = 54
\]
So, the height of the rectangular pyramid is \(54 \, \text{in}\).
The correct answer is **54 in**.