Question
A rectangular prism has a base area of 15 cm2
, and pyramid with a congruent base and height has a volume of 20 cm3
. What is the height of the rectangular prism?(1 point)
Responses
20 cm
20 cm
4 cm
4 cm
5 cm
5 cm
4/3 cm
, and pyramid with a congruent base and height has a volume of 20 cm3
. What is the height of the rectangular prism?(1 point)
Responses
20 cm
20 cm
4 cm
4 cm
5 cm
5 cm
4/3 cm
Answers
GPT-4o mini
To find the height of the rectangular prism, we first need to recall the formula for the volume of a rectangular prism, which is given by:
\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]
We know the base area of the prism is \(15 \, \text{cm}^2\), and we want to determine the height \(h\).
Given that we have the volume of the rectangular prism, we can use the given information about the pyramid. The volume of the pyramid with a congruent base and the same height is given by the formula:
\[
\text{Volume of Pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The problem states that the volume of the pyramid is \(20 \, \text{cm}^3\). Thus, we can set up the equation as follows:
\[
20 \, \text{cm}^3 = \frac{1}{3} \times 15 \, \text{cm}^2 \times h
\]
Multiplying both sides by \(3\) to eliminate the fraction:
\[
60 \, \text{cm}^3 = 15 \, \text{cm}^2 \times h
\]
Now, dividing both sides by \(15 \, \text{cm}^2\):
\[
h = \frac{60 \, \text{cm}^3}{15 \, \text{cm}^2} = 4 \, \text{cm}
\]
Thus, the height of the rectangular prism is:
\[
\boxed{4 \, \text{cm}}
\]
\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]
We know the base area of the prism is \(15 \, \text{cm}^2\), and we want to determine the height \(h\).
Given that we have the volume of the rectangular prism, we can use the given information about the pyramid. The volume of the pyramid with a congruent base and the same height is given by the formula:
\[
\text{Volume of Pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The problem states that the volume of the pyramid is \(20 \, \text{cm}^3\). Thus, we can set up the equation as follows:
\[
20 \, \text{cm}^3 = \frac{1}{3} \times 15 \, \text{cm}^2 \times h
\]
Multiplying both sides by \(3\) to eliminate the fraction:
\[
60 \, \text{cm}^3 = 15 \, \text{cm}^2 \times h
\]
Now, dividing both sides by \(15 \, \text{cm}^2\):
\[
h = \frac{60 \, \text{cm}^3}{15 \, \text{cm}^2} = 4 \, \text{cm}
\]
Thus, the height of the rectangular prism is:
\[
\boxed{4 \, \text{cm}}
\]