Looking at the diagram, we know that the diameter of the cone's base is 4.5 centimeters. By dividing by 2, we get the radius of the base.
r=4.5/2 ⇔ r= 2.25cm
We now know that the radius of the cone is 2.25 centimeters and that the height of the cone is 12 centimeters. Now, we can focus on the right triangle created within the cone.
The slant height of the cone is the hypotenuse of the triangle. The legs of the triangle are the height of the pyramid h and the radius r of the base. Notice that we can find the slant height of the cone using the Pythagorean Theorem.
h^2+ r^2= l^2
Let's substitute 12 for h and 2.25 for r into the above equation to find the slant height of the cone.
We found that the slant height is about 12.2 centimeters. Note that, when solving the above equation, we only kept the principal root because l represents a side length and must be a positive number. Let's now substitute r with 2.25 and l with 12.2 into the formula, we can calculate S.
