Question
A rectangular pyramid has a volume of 10 cm3
. What is the volume of a rectangular prism given it has a congruent base and height to the pyramid?(1
. What is the volume of a rectangular prism given it has a congruent base and height to the pyramid?(1
Answers
GPT-4o mini
The volume \( V \) of a pyramid can be calculated using the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
For a rectangular prism with the same base area and height as the pyramid, the volume \( V \) of the prism is calculated using the formula:
\[
V = \text{Base Area} \times \text{Height}
\]
Since the volume of the pyramid is given as \( 10 \, \text{cm}^3 \), we can express the volume of the prism in terms of the volume of the pyramid.
If we denote the base area as \( A \) and the height as \( h \), the volume of the pyramid is:
\[
10 = \frac{1}{3} \times A \times h
\]
To find the volume of the prism:
\[
V_{\text{prism}} = A \times h
\]
We can find \( A \times h \) from the pyramid's volume equation:
\[
V_{\text{prism}} = 3 \times 10 = 30 \, \text{cm}^3
\]
Therefore, the volume of the rectangular prism is \( 30 \, \text{cm}^3 \).
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
For a rectangular prism with the same base area and height as the pyramid, the volume \( V \) of the prism is calculated using the formula:
\[
V = \text{Base Area} \times \text{Height}
\]
Since the volume of the pyramid is given as \( 10 \, \text{cm}^3 \), we can express the volume of the prism in terms of the volume of the pyramid.
If we denote the base area as \( A \) and the height as \( h \), the volume of the pyramid is:
\[
10 = \frac{1}{3} \times A \times h
\]
To find the volume of the prism:
\[
V_{\text{prism}} = A \times h
\]
We can find \( A \times h \) from the pyramid's volume equation:
\[
V_{\text{prism}} = 3 \times 10 = 30 \, \text{cm}^3
\]
Therefore, the volume of the rectangular prism is \( 30 \, \text{cm}^3 \).