A rectangular Pyramid has a base area of 16in., and a congruent rectangular prism has a volume of 288 in.What is the height of the rectangular Pyramid?
We can start by using the formula for the volume of a rectangular prism:
Volume of rectangular prism = Base area × Height
We are given that the volume of the prism is 288 in, and the base area is 16 in, so we can substitute those values into the formula:
288 = 16 × Height
Solving for Height, we can divide both sides by 16:
Height = 288 ÷ 16
Height = 18
Therefore, the height of the rectangular pyramid is 18 inches.
To find the height of the rectangular pyramid, we need to use the formula for the volume of a pyramid. The formula is:
Volume of a pyramid = (1/3) * base area * height
Given information:
Base area of the pyramid = 16 in²
Volume of the congruent rectangular prism = 288 in³
We know that the rectangular prism is congruent to the pyramid, meaning they have the same dimensions. Therefore, the base area of the rectangular prism is also 16 in².
Let's solve for the height of the pyramid:
(1/3) * 16 in² * height = 288 in³
Multiplying both sides by 3 to cancel out the fraction:
16 in² * height = 3 * 288 in³
16 in² * height = 864 in³
Dividing both sides by 16 in² to solve for height:
height = 864 in³ / 16 in²
height = 54 in
Therefore, the height of the rectangular pyramid is 54 inches.