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 and Hot congruent to the prism what is the height of the pyramid
To find the height of the rectangular pyramid, we first need to determine the dimensions of the base of the prism.
Given that the base area of the prism is 25 in², we can find the length and width of the base by taking the square root of the base area.
Let the length of the base be L and the width of the base be W.
Then, L * W = 25 in²
Since the base is congruent, L = W
From L * W = 25, we can substitute L for W
L * L = 25
L² = 25
L = 5 inches
Therefore, the base of the prism is a square with sides of length 5 inches.
Now, to find the height of the prism, we can use the formula for the volume of a rectangular prism:
Volume = base area * height
125 in³ = 25 in² * height
height = 125 in³ / 25 in²
height = 5 inches
The height of the prism is 5 inches.
Since the rectangular pyramid has the same base and volume as the prism, the height of the pyramid is also 5 inches.