Arectangular pyramid has a base with dimensions 5 inches by 7 inches. the height of the pyramid is unknown. if the volume of the pyramid is 105 cubic inches, what is the height of the pyramid? explain the steps

The height of the pyramid is 9 inches.

A rectangular pyramid is a three dimensional object that has a rectangular base and triangular faces that correspond to each side of the rectangular base.

The volume of a rectangular pyramid = 1/3 .x length x width x height

In order to determine the height of the rectangular pyramid, divide the given volume by 1/3 and the area of the base of the rectangular pyramid.

Height = 105 / (1/3 x 5 x 7) = 9 inches

To learn more about pyramids, please check: link

The height of the pyramid is

Step-by-step explanation:

we know that

The volume of the rectangular pyramid is equal to

where

B is the area of the rectangular base of the pyramid

H is the height of the pyramid

Find the area of the base B

we have

substitute the value of B and the value of V in the formula and solve for H

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11