The given solid is a cone with a diameter of 16.5 feet and a slant height of 9.5 feet. To calculate the lateral area, we must 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 rlIn this formula, r is the radius and l is the slant height of the cone. We know that the diameter of the cone's base is 16.5 feet. By dividing by 2, we get the radius of the base.
r=16.5/2 ⇒ r= 8.25ft
We now know that the radius of the cone is 8.25ft and that the slant height of the cone is 9.5ft. With this information we are able to calculate the lateral area of the cone. To do so, we will substitute r= 8.25 and l= 9.5 into the formula for the lateral area. Let's do it!
