The surface area of a cone with height and radius (of its top) is given by . If the radius of the top is held constant, the surface area is proportional to:
D)None of the above.

Question

The surface area of a cone with height and radius (of its top) is given by . If the radius of the top is held constant, the surface area is proportional to:   
D)None of the above.

Quizplus · Accepted Answer

The surface area of a cone is given by $\pi r \sqrt{r^2+h^2}$, where $r$ is the radius of the top and $h$ is the height. If we hold $r$ constant, then the surface area is proportional to $\sqrt{r^2+h^2}$. Therefore, as we increase $h$, the surface area will increase proportionally. So, the correct answer is (B), which is the only option that includes $\sqrt{r^2+h^2}$ in it.

The Surface Area of a Cone with Height and Radius