+1552 A right cone has a radius of 10 and a height of $20.$ Let $A$ and $B$ be diametrically opposite points on the base, and let $C$ be the midpoint of $B$ and the apex of the cone. A bug crawls from $A$ to $C$ on the surface of the cone. What is the length of the shortest path it can take?
+130031 Here's my best attempt ???
If we "unroll" the cone we have the following triangle, ADB
Circumference of the cone = triangle base = 2pi * radius of cone = 2pi * 10 = 20 pi = AB
So
A = (-10pi , 0)
B = (10pi , 0)
D = height of the cone = (0, 20)
C = (5pi ,10)
The shortest distance from A to C = sqrt [(-10 pi -5pi)^2 + ( (20 -10)^2] =
sqrt [ 225pi^2 + 100] ≈ 48.17
