Surface Area of a Right Circular Cone

A right circular cone has a base radius of 6 cm and a height of 8 cm. Another cone is similar to this cone, but its height is 12 cm. What is the surface area of the larger cone?

To find the surface area of a cone, you can use the formula:

$$ SA = rac{1}{2} imes 2 imes ext{π} imes r imes l + ext{π} imes r^2 $$

where $r$ is the base radius, and $l$ is the slant height of the cone. The slant height $l$ can be calculated using the Pythagorean theorem:

$$ l = ext{√}(r^2 + h^2) $$