Question

A solid cylinder and a solid cone have equal base and equal height. If the radius and the height are in the ratio of $4:3,$ then total surface area of the cylinder to that of the cone are in the ratio

• A. $\frac{14}{11}$
• B. $\frac{14}{9}$
• C. $\frac{9}{14}$
• D. $\frac{9}{11}$

Answer 1

The correct option is B $\frac{14}{9}$

Let radius be $4x$ and height be $3x.$

Now, $\frac{2\pi rh+2\pi r^2}{\pi rl+\pi r^2}$
$=\frac{2(h+r)}{\sqrt{r^2+h^2}+r}$
$=\frac{2\left(7x\right)}{\sqrt{16x^2+9x^2}+4x}$
$=\frac{14}{9}$