The lateral surface area S of a right circular cone is given by (equation given below). What radius should be used to produce a cone of height 5 inches and lateral surface area 100 square inches?

a. r = 1.52138.

b. r = 4.658

c. r = 78

d. r = 6.7432

Given:

Lateral Area = π * r * (√h² + r²)

Lateral Area = 100 in²; height = 5 in

I find it hard to derive the formula of r because of the radical sign. So, I'll just plug each radius to the formula to check confirm the given lateral area.

a) r = 1.52138 ⇒ LA = 24.98

b) r = 4.658 ⇒ LA = 100

c) r = 78 ⇒ LA = 19152.68

d) r = 6.7432 ⇒ LA = 177.84

The radius is B.) r = 4.658 inches