If the area of the base of a right circular cone is 9856 cm2 and its height is 33 cm, what is the curved surface area of the cone?

To find the curved surface area of a cone, we first need to find the radius of the base of the cone. We know that the area of the base (which is a circle) is given by the formula:

Area = πr²

We know the area is 9856 cm². So we can set up the equation:

9856 = πr²

To solve for r, we divide both sides by π:

r² = 9856 / π

Then, take the square root of both sides to solve for r:

r = sqrt(9856 / π)

Next, we need to find the slant height (l) of the cone. This can be found using the Pythagorean theorem, since a right circular cone forms a right triangle from the apex to the base. The formula is:

l = sqrt(r² + h²)

where h is the height of the cone. Plug in the values we know:

l = sqrt((sqrt(9856 / π))² + 33²)

Finally, we can find the curved surface area (A) of the cone using the formula:

A = πrl

Plug in the values we know:

A = π * sqrt(9856 / π) * sqrt((sqrt(9856 / π))² + 33²)

This will give you the curved surface area of the cone.