To calculate the volume of a cone, we can use the following formula, where r is a radius and h is a height.
V= 13Ï€ r^2 h
In our exercise we are given that the slant height of a cone is 25 meters and a radius is 15 meters.
Now notice that a slant height, radius and a height h form a right triangle. Let's focus on this triangle for a little bit.
As we can see, to calculate the height of the cone, we can use the Pythagorean Theorem. Let's write an equation according to this theorem.
h^2+15^2=25^2
Now let's solve this equation for h.
Note that, when solving the above equation, we only needed to consider the principal root because h is a positive number.
We are given that the radius is 15m and we found that the height of the cone is 20m. Let's substitute these values into the volume formula.
