Answer:
3024π square inches
Explanation:
The surface area is the sum of ...
- lateral area of the cone
- lateral area of the cylinder
- area of the circular base
The relevant area formulas are ...
A = πrs . . . . . lateral area of cone with radius r and slant height s
A = 2πrh . . . . lateral area of cylinder with radius r and height h
A = πr² . . . . . area of a circle of radius r
The radius is half the diameter, so is (36 in)/2 = 18 in. When we add up these areas, we can factor out a common factor to simplify the expression a bit.
A = πrs +2πrh +πr²
A = πr(s +2h +r) = π(18 in)(30 in +2(60 in) +18 in) = π(18)(168) in²
A = 3024π in² . . . . surface area