Question

The height and base radius of a cone are increased by a factor of 2 to create a similar cone. How is the slant height of the cone affected?

The slant height of the larger cone is equal to the slant height of the smaller cone.
The slant height of the larger cone is double the slant height of the smaller cone.
The slant height of the larger cone is 4 times the slant height of the smaller cone.
The slant height of the larger cone is 8 times the slant height of the smaller cone.

Answer 1

The slant height is doubled.

Reason: l = sqrt(r^2 + h^2). If r and h are multiplied by 2, l' = sqrt((2r)^2 + (2h)^2) = sqrt(4(r^2 + h^2)) = 2l.