Question

What change will double the lateral surface area of a cone

Answer 1

To double the lateral surface area of a cone, increase the slant height by a factor of the square root of 2 (√2).

Step-by-step explanation:

To double the lateral surface area of a cone, we need to increase the slant height of the cone by a factor of √2 (square root of 2).

The lateral surface area of a cone can be calculated using the formula:

Lateral Surface Area = πrL, where r is the radius of the base and L is the slant height.

By increasing the slant height by a factor of √2, the lateral surface area will double.

Answer 2

The lateral surface area of a cone is

(pi) x (radius of the base) x (slant height) .

You can't double pi. But if you double the radius of the base
and keep the same slant height, OR double the slant height
and keep the same radius, then the lateral area will double.

More generically . . . if you increase the radius and the slant
height in any way that doubles their product, then the lateral
area doubles.