What is the area of cone???

The first step in finding the surface area of a cone is to measure the radius of the circle part of the cone. The next step is to find the area of the circle, or base. The area of a circle is 3.14 times the radius squared (πr2). Now, you will need to find the area of the cone itself. In order to do this, you must measure the side (slant height) of the cone. Make sure you use the same form of measurement as the radius. You can now use the measurement of the side to find the area of the cone. The formula for the area of a cone is 3.14 times the radius times the side (πrl). So the surface area of the cone equals the area of the circle plus the area of the cone and the final formula is given by: SA = πr2 + πrl Where, r is the radius h is the height l is the slant height The area of the curved (lateral) surface of a cone = πrl Note: A cone does not have uniform (or congruent) cross-sections. (more about conic section here) Example 1: A cone has a radius of 3cm and height of 5cm, find total surface area of the cone. Solution: To begin with we need to find slant height of the cone, which is determined by using Pythagoras, since the cross section is a right triangle. l2 = h2 + r2 l2 = 52 + 32 l2 = 25 + 9 l = √(34) l = 5.83 cm And the total surface area of the cone is: SA = πr2 + πrl SA = π · r · (r + l) SA = π · 3 · (3 + 5.83) SA = 83.17 cm2 Therefore, the total surface area of the cone is 83.17cm2