Question

A right pyramid has a square base with sides of length 14 units.

Each segment connecting the apex to a midpoint of a side of the base has length 25 units.
What is the volume of the pyramid?
cubic units

Answer 1

Explanation:

To find the volume of a pyramid, we can use the formula:

V = (1/3) * base area * height

First, we need to find the height of the pyramid. To do this, we can draw a diagram of the pyramid and create a right triangle using half a side of the base, the height of the pyramid, and one of the segments connecting the apex to a midpoint of a side of the base.

Using the Pythagorean theorem, we can solve for the height:

h^2 + (14/2)^2 = 25^2

h^2 + 49 = 625

h^2 = 576

h = 24

Now we can find the base area:

Base area = 14^2

Base area = 196

And finally, we can use the formula to find the volume:

V = (1/3) * 196 * 24

V = 1568 cubic units

Therefore, the volume of the pyramid is 1568 cubic units.