Answer
The surface of cone is not equal to $\dfrac{1}{3}$ rd of cylinder.
Work Step by Step
The surface area of cone is equal to $S(cone)=\pi r \sqrt {r^2+h^2}$ and the surface area of cylinder is equal to $S(cylinder)=2 \pi r h$
Now, $\dfrac{S(cone)}{S(cylinder)}=\dfrac{\pi r \sqrt {r^2+h^2}}{2 \pi r h}$
This implies that
$\dfrac{S(cone)}{S(cylinder)}=\dfrac{1}{2} \sqrt {1+\dfrac{r^2}{h^2}}$
We conclude that the surface of cone is not equal to $\dfrac{1}{3}$ rd of cylinder.
