Question

Give step by step instructions and the final answer on how to find the volume of a right square pyramid who has a slant height of 5 inches and the length of the base is 4 inches.

To earn full points you must :

- Show each step of your work

- Keep it organized and easy to read

- Give a brief explanation of why you perform each step

- give the correct final answer

Answer 1

Answer:

Below.

Step-by-step explanation:

First find the perpendicular  height of the pyramid.

The median of one of the faces, the height and  and half the length of the square base make a right triangle with base 2 and hypotenuse 5, so using the Pythagoras theorem:

5^2 = 2^2 + h^2

h^2 = 5^2 - 2^2 = 21

h = √21 inches.

The volume of the pyramid V = 1/3 * h * area of the base, so

V = 1/3 * 4^2 * √21

= 24.44 in^3 to nearest hundredth.