The lateral surface area s of a right circular cone is given by 649-01-06-00-00_files/i018.jpg. what radius should be used to produce a cone of height 5 inches and lateral surface area 100 square inches?

Hi, thank you for posting your question here at .

The lateral surface area (S) of a circular cone has the equation:

S = pi*r*l, where l is the slant height. The slant height is the hypotenuse of a right triangle with the radius of the cone and the height of the cone as its two other legs. 

l2 = r^2 + h^2
l = sqrt(r^2 + (5)^2)
l = sqrt(r^2 + 25), substituting this to the equation:

100 = pi*r*[sqrt(r^2 + 25)]
Therefore, r = 4.66 inches.