Volume Unit Test
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Question
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?(1 point)
in.3
The volume of a rectangular pyramid is given by the formula V = (1/3) * base area * height.
In this case, the volume of the pyramid is 480 in^3. Since the base and height of the prism are congruent to the pyramid, the base area of the prism would be the same as the base area of the pyramid.
Let's say the base area of the prism is x in^2. Then, using the formula for the volume of a rectangular prism (V = base area * height), the volume of the prism would be x * 3.
Since the volume of the pyramid is 480 in^3, we can set up the equation:
480 = (1/3) * x * height
Solving for x:
480 = (1/3) * x * height
x = 1440 / height
Therefore, the volume of the prism would be:
V = x * height
V = (1440 / height) * 3
V = 1440
So the volume of the rectangular prism would be 1440 in^3.