How to find the slant height of a cone when given SA and radius?

Question

"What is the slant height of a cone if the surface area is 18.6 in ² with a radius of 1.2 in.? Enter a number answer only. round answer to the nearest tenth"

Answer 1

Surface area of cone = Area of base + Curved surface area

= pi*r*r + pi*r*l

where r is the radius and l is the slant height.

Substituting the values in the equation above, we have

18.6 = pi*(1.2)(1.2) + pi*(1.2)*l

18.6 - pi*(1.2)(1.2) = pi*(1.2)*l

14.076 = pi*(1.2)*l

l = 14.076/(pi*1.2)

= 3.73

Hence, the slant height is 3.7in