A rectangular pyramid has a volume of 480 in.3 . If a rectangular prism has a base and height congruent to the pyramid, what is the volume of the prism?
Since the base and height of the rectangular prism are congruent to the triangular pyramid, we can assume that the base area of the prism is the same as the base area of the pyramid.
The formula for the volume of a rectangular pyramid is given as:
\[V = \frac{1}{3} \times \text{base area} \times \text{height}\]
Given that the volume of the pyramid is 480 in.3, we can plug in the values:
\[480 = \frac{1}{3} \times \text{base area} \times \text{height}\]
\[480 = \frac{1}{3} \times \text{base area} \times \text{base height}\]
\[1440 = \text{base area} \times \text{base height}\]
To find the volume of the prism, we also use the formula:
\[V = \text{base area} \times \text{height}\]
Since the base area of the prism is the same as that of the pyramid, the volume of the prism will be:
\[V = 1440 \times \text{height}\]
Without knowing the height of the prism, we cannot calculate its volume. The volume of the prism would depend on the height that is given in the problem.
so what is the answer?
I apologize for the confusion. Let's calculate the volume of the rectangular prism.
Given that the volume of the rectangular pyramid is 480 in.3 and the formula for the volume of a rectangular pyramid is:
\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]
Since the volume is given as 480 in.3, we know that the base area times the height is 1440. The base area times the height of the rectangular prism is equal to the volume of the rectangular pyramid.
Now, if the base and height of the rectangular prism are congruent to the triangular pyramid, then the volume of the rectangular prism will also be 480 in.3.
Therefore, the volume of the rectangular prism is 480 in.3.