Hi, thank you for posting your question here at Brainly.
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.
