We know that the lateral area of a right cone is half the product of the circumference of the base and the slant height.
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. Since the diameter of the base is 4 meters, we have that its radius is 4÷ 2=2 meters.
In this right triangle, the legs are 4.5 and 2 meters 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 sqrt(24.25) meters long.
With this information we are able to calculate the lateral area of the cone. Substitute r=2 and l=sqrt(24.25) into the formula for the lateral area. Let's do it!
