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. Since the volume of the pyramid is 480 in^3, we can set up the equation:
480 = (1/3) * base area * height
Since the base and height of the prism are congruent to the pyramid, the base area and height of the prism will be the same. Let's denote the base area as B and the height as H. Therefore, the volume of the prism will be V = B * H.
From the equation above, we can solve for the base area:
480 = (1/3) * B * H
B * H = 480 * 3
B * H = 1440
Now, since the base and height are congruent, we can set H = B:
B^2 = 1440
B = sqrt(1440)
B = 38.08 in^2
Now, we can find the volume of the prism:
V = B * H
V = 38.08 * 38.08
V ≈ 1,451.15 in^3
Therefore, the volume of the prism is approximately 1,451.15 in^3.
are you sure its correct
Let's verify the answer for the volume of the rectangular prism:
The base area of the pyramid (B) can be found using the formula for the volume of a rectangular pyramid:
V = (1/3) * B * H
480 = (1/3) * B * H
B * H = 480 * 3
B * H = 1440
Since the base area and height are congruent in the rectangular prism, we have B = H.
Therefore, B^2 = 1440
B = sqrt(1440)
B = 37.95 in^2 (approximately)
Now, the volume of the rectangular prism can be calculated:
V = B * B * H
V = 37.95 * 37.95 * 37.95
V ≈ 54406.89 in^3
Therefore, the correct volume of the rectangular prism with a base and height congruent to the pyramid would be approximately 54,406.89 in^3.
whats the exact answer
To find the exact answer, we can use the volume formula for a rectangular prism:
Given:
Base area (B) = 38.08 square inches
Height (H) = 38.08 inches
Volume of the rectangular prism:
V = B * H * H
V = 38.08 * 38.08 * 38.08
V = 55,431.09 cubic inches
Therefore, the exact volume of the rectangular prism is 55,431.09 cubic inches.