Question
There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is
48 in
.
3
48 in.3, what is the volume of the prism?(1 point)
Responses
24 in
.
3
24 in.3
24 in. cubed
144 in
.
3
144 in.3
144 in. cubed
96 in
.
3
96 in.3
96 in. cubed
16 in
.
3
48 in
.
3
48 in.3, what is the volume of the prism?(1 point)
Responses
24 in
.
3
24 in.3
24 in. cubed
144 in
.
3
144 in.3
144 in. cubed
96 in
.
3
96 in.3
96 in. cubed
16 in
.
3
Answers
GPT-4o mini
The volume of a pyramid is given by the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The volume of a rectangular prism is given by the formula:
\[
V = \text{Base Area} \times \text{Height}
\]
Since both the prism and the pyramid have congruent bases and heights, the volume of the prism can be calculated based on the pyramid's volume. Specifically, since the volume of the pyramid is one-third that of the prism, we can express the volume of the prism as:
\[
\text{Volume of the prism} = 3 \times \text{Volume of the pyramid}
\]
Given that the volume of the pyramid is 48 in³:
\[
\text{Volume of the prism} = 3 \times 48 \, \text{in}^3 = 144 \, \text{in}^3
\]
Therefore, the volume of the prism is:
\[
\boxed{144 \, \text{in}^3}
\]
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The volume of a rectangular prism is given by the formula:
\[
V = \text{Base Area} \times \text{Height}
\]
Since both the prism and the pyramid have congruent bases and heights, the volume of the prism can be calculated based on the pyramid's volume. Specifically, since the volume of the pyramid is one-third that of the prism, we can express the volume of the prism as:
\[
\text{Volume of the prism} = 3 \times \text{Volume of the pyramid}
\]
Given that the volume of the pyramid is 48 in³:
\[
\text{Volume of the prism} = 3 \times 48 \, \text{in}^3 = 144 \, \text{in}^3
\]
Therefore, the volume of the prism is:
\[
\boxed{144 \, \text{in}^3}
\]