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.
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
3 answers
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.
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.
3 answers