A rectangular prism has a base area of 25 in.² and a volume of 125 in.³ if a rectangular pyramid has a congruent base in height congruent to the prism what is the height of the pyramid
To find the height of the pyramid, we need to first determine the dimensions of the base of the prism. Since the base area of the prism is 25 in², and it is a rectangle, we can find the dimensions by taking the square root of the base area.
√25 = 5
So, the base of the prism has dimensions of 5 in x 5 in.
Next, we can find the height of the prism by dividing the volume by the base area:
125 in³ / 25 in² = 5 in
Therefore, the height of the prism is 5 inches.
Since the base of the pyramid is congruent to the base of the prism, the base of the pyramid also has dimensions of 5 in x 5 in.
Finally, we can find the height of the pyramid by using the volume formula for a pyramid:
Volume = (1/3) x base area x height
125 in³ = (1/3) x 25 in² x height
125 in³ = 8.33 in² x height
height = 125 in³ / 8.33 in² ≈ 15 inches
Therefore, the height of the pyramid is approximately 15 inches.