A solid cone and a solid cylinder have equal base and equal height. If the radius and height be in the ratio of 12 : 5, the ratio of the total surface area of cone to that of the cylinder is
Solution
✅ Correct Option: 4
Let $r=12k$ and $h=5k$. The cone needs its slant height, found by Pythagoras: $l=\sqrt{r^2+h^2}=\sqrt{144k^2+25k^2}=\sqrt{169k^2}=13k$ | Solid | Total surface area formula | Value | |---|---|---| | Cone | $\pi r(r+l)$ | $\pi(12k)(12k+13k)=300\pi k^2$ | | Cylinder | $2\pi r(r+h)$ | $2\pi(12k)(12k+5k)=408\pi k^2$ | $\text{Ratio}=\dfrac{300\pi k^2}{408\pi k^2}=\dfrac{300}{408}=\dfrac{25}{34}$ So the ratio is $25:34$.