Question

Find the volume of the following. Please round your answer to the nearest tenth. Please do not put units. Hint: You need to use the pythagorean theorem

Answer 1

V = 1,568

Explanation:

The Volume of a Square Pyramid

Given a square-based pyramid of base side a and height h, the volume can be calculated with the formula:

`\displaystyle V=(1)/(3)a^2h`

We are given a square pyramid with a base side a=14 ft but we're missing the height. It can be calculated by using the right triangle shown in the image attached below, whose hypotenuse is 25 ft and one leg is 7 ft

We use Pythagora's theorem:

`25^2=h^2+7^2`

Solving for h:

`h^2=25^2-7^2=625-49=576`

`h=√(576)=24`

The height is h=24 ft. Now the volume is calculated:

`\displaystyle V=(1)/(3)*14^2*24`

V = 1,568