What change will triple the lateral surface area of a cone?

Answer 1

To triple the lateral surface area of a cone, you must increase the radius while keeping the height constant. The lateral surface area ( A ) of a cone is given by the formula ( A = \pi r l ), where ( r ) is the radius and ( l ) is the slant height. Since the slant height is related to both the radius and the height, adjusting the radius proportionately will achieve the desired increase in surface area. Specifically, you need to increase the radius by a factor of ( \sqrt{3} ) while maintaining the same height.