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?
? in.3
Since the volume of a pyramid is given by the formula V = (1/3) * base area * height, we can find the base area of the pyramid by rearranging the formula to: base area = 3 * V / height = 3 * 480 / height = 1440 / height.
Since the base of the prism is congruent to the base of the pyramid, the volume of the prism will be the base area multiplied by the height of the prism: V = 1440 / height * height = 1440 in.3.
Therefore, the volume of the prism is 1440 in.3.
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Let me correct my mistake.
Since the pyramid has a volume of 480 in^3, and it's a rectangular pyramid, which means the base is a rectangle. The volume of a rectangular pyramid is given by the formula V = (1/3) * base area * height.
If the volume of the pyramid is 480 in^3, then we have:
480 = (1/3) * base area * height
Since the base of the pyramid is a rectangle, the base area is length * width.
Let's say the base area is x * y, and the heigh of the pyramid is z. Then we can write:
480 = (1/3) * x * y * z
We know that the base and height of the prism are congruent to the base and height of the pyramid. Therefore, the volume of the prism will be x * y * z.
So, we have:
Volume of the prism = x * y * z = 480 * 3 = 1440 in^3
Therefore, the volume of the prism is 1440 in^3.