Question

An ant is sitting at the periphery of the base of cone of slant height h and radius a. The length of the shortest path for the ant to move around the surface of the cone without ever leaving it and return to its original position is,

Answer 1

Answer:

Shortest distance = 6

Step-by-step explanation:

The radius of the cone will be 1

Thus, the circumference of cone = 2π

Unfolding the cone  will result in a sector with radius 6 and circular circumference 2π. Labelling the center O  and the other two vertices A and B.The full circle has a circumference of 12π, thus the sector is a 2π/12π × 360° = 60°

Thus, the sector is 60°, so that ABO will be an equilateral triangle and the shortest distance will be AB = 6. Thus, The length of the shortest path for the ant to move around the surface of the cone without ever leaving it and return to its original position is 6.