We know that the lateral area of a right cone is half the product of the circumference of the base and the slant height of the cone.
L.A.=1/2* 2π r* l ⇔ L.A.=π rl
In this formula, r is the radius and l is the slant height of the cone. Although we do not have the slant height, we can find it by using the Pythagorean Theorem. We have that radius of the base is 3 centimeters.
In this right triangle, the legs are 3 and 4 centimeters long. The hypotenuse is l. We will substitute these values in the Pythagorean Theorem and solve for l.
The hypotenuse of the right triangle, and therefore the slant height of the cone, is 5 centimeters long.
With this information, we are able to calculate the lateral area of the cone. Substitute r=3 and l=5 into the formula for the lateral area. Let's do it!
