The slant height of a cone is increased by 10% and its radius is doubled. What is the percentage increase in the surface area of the cone?

To find the percentage increase in the surface area of the cone, we need to compare the original surface area with the new surface area after the given changes.

Let's assume the original slant height of the cone is "s" and the original radius is "r". Therefore, the original surface area of the cone can be calculated using the formula:

Original Surface Area = π * r * (r + s)

Now, according to the given information, the slant height is increased by 10%, which means the new slant height is 1.1 times the original slant height (1 + 10% = 1.1). Additionally, the radius is doubled, so the new radius is 2 times the original radius.

Therefore, the new slant height is 1.1s and the new radius is 2r. Using these new values, we can calculate the new surface area of the cone:

New Surface Area = π * (2r) * (2r + 1.1s)

To find the percentage increase in the surface area, we can use the following formula:

Percentage Increase = ((New Surface Area - Original Surface Area) / Original Surface Area) * 100

Substituting the values, we get:

Percentage Increase = ((π * (2r) * (2r + 1.1s) - π * r * (r + s)) / (π * r * (r + s))) * 100

Simplifying the equation, we get:

Percentage Increase = ((4r^2 + 2.2rs) - (r^2 + rs)) / (r^2 + rs) * 100

Percentage Increase = (3r^2 + 1.2rs) / (r^2 + rs) * 100

Therefore, the percentage increase in the surface area of the cone is (3r^2 + 1.2rs) / (r^2 + rs) * 100.