MATH214
posted by Rebecca on .
Find the surface area of a right circular cone topped with a hemisphere. the height of the cone is 8cm, the radius is 4cm.

here's the formula SA = pr^2 + prL

I think we are looking at something like a single scoop icecream cone, right?
The surface area of a cone is pi(r)(s) where r is the radius and s is the slant height.
The surface area of a hemisphere
= (1/2)4pi(r^2) = 2pi(r^2)
we find s by using Pythagoras:
s^2 = 8^2 + 4^2 = 80
s = √80
So total surface area
= pi(4)√80 + 2pi(4^2)
= pi(16√5) + 32pi or appr. 212.93
check my arithmetic, its been horrible lately.