a rectangular prism has a volume of 25 in. ^2 and a volume of 125 in. ^3. In a rectangular pyramid has a base and height congruent to the pyramid, what is the height of the pyramid
If the volume of the rectangular prism is 125 in.^3, this means that the base area of the prism is 25 in.^2 and the height of the prism is 5 in., since 25 * 5 = 125.
Since the base and height of the rectangular pyramid are congruent to those of the rectangular prism, the base area of the pyramid is also 25 in.^2.
To find the height of the pyramid, we can use the formula for the volume of a pyramid, which is V = (1/3) * base area * height.
Substitute the values we know:
125 = (1/3) * 25 * height
Simplify:
125 = 8.33 * height
Divide both sides by 8.33:
height ≈ 15
Therefore, the height of the rectangular pyramid is approximately 15 inches.
the correct answer is 5 thanks though
I apologize for the mistake. Let me correct my solution:
Since the volume of the rectangular prism is 125 in.^3 and the base area of the prism is 25 in.^2, the height of the prism is 5 in.
Since the base and height of the rectangular pyramid are congruent to those of the rectangular prism, the base area of the pyramid is also 25 in.^2.
Let's use the formula for the volume of a pyramid:
V = (1/3) * base area * height
125 = (1/3) * 25 * height
125 = 25/3 * height
125 = 8.33 * height
To find the height of the pyramid:
height = 125 / 8.33
height ≈ 15
Therefore, I made an error in my initial response. The correct height of the rectangular pyramid is indeed approximately 15 inches. Thank you for the correction.