Question
There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is 48 in.3 , what is the volume of the prism?(1 point)
Responses
16 in.3
16 in. cubed
144 in.3
144 in. cubed
24 in.3
24 in. cubed
96 in.3
Choose the best answer pls
Responses
16 in.3
16 in. cubed
144 in.3
144 in. cubed
24 in.3
24 in. cubed
96 in.3
Choose the best answer pls
Answers
GPT-4o mini
The volume of a pyramid is given by the formula:
\[
V_{pyramid} = \frac{1}{3} \times B \times h
\]
where \(B\) is the area of the base and \(h\) is the height. The volume of a rectangular prism is given by:
\[
V_{prism} = B \times h
\]
Since the pyramid and the prism have congruent bases and equal heights, we can relate their volumes. The volume of the prism is three times the volume of the pyramid:
\[
V_{prism} = 3 \times V_{pyramid}
\]
In this case, the volume of the pyramid is given as 48 in³:
\[
V_{prism} = 3 \times 48 \, \text{in}^3 = 144 \, \text{in}^3
\]
So, the volume of the prism is **144 in³**.
Thus, the best answer is **144 in.³**.
\[
V_{pyramid} = \frac{1}{3} \times B \times h
\]
where \(B\) is the area of the base and \(h\) is the height. The volume of a rectangular prism is given by:
\[
V_{prism} = B \times h
\]
Since the pyramid and the prism have congruent bases and equal heights, we can relate their volumes. The volume of the prism is three times the volume of the pyramid:
\[
V_{prism} = 3 \times V_{pyramid}
\]
In this case, the volume of the pyramid is given as 48 in³:
\[
V_{prism} = 3 \times 48 \, \text{in}^3 = 144 \, \text{in}^3
\]
So, the volume of the prism is **144 in³**.
Thus, the best answer is **144 in.³**.