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 pyramid is given by the formula V = (1/3) * B * h, where B is the area of the base and h is the height of the pyramid.
Since the volume of the pyramid is 480 in.3 and the base and height are congruent to those of the prism, we can set up the equation:
480 = (1/3) * B * h
Since the base and height of the prism are the same as those of the pyramid, we can rewrite the equation as:
480 = (1/3) * B * B * B
480 = (1/3) * B^2 * B
480 = (1/3) * B^3
1440 = B^3
Taking the cube root of both sides, we get:
B = 12 inches
Now that we know the base of the prism, we can find the volume by multiplying the base area by the height of the prism:
V = B * B * B = 12 * 12 * 12 = 1728 in.3
Therefore, the volume of the rectangular prism is 1728 in.3.