Question

The ratio of total surface area to curved surface of the cone is 8:5. Then the ratio of radius to height is____.

• A. 7:6
• B. 2:3
• C. 3:4
• D. 5:4

Answer 1

The correct option is C 3:4

We know that,
Total surface area of cone
$=\pi r(r+l)$
Curved surface area of cone
$=\pi rl$

Hence, the required ratio
$=\frac{Totalsurfaceareaofcone}{Curvedsurfacearea}$

$=\frac{\pi r(r+l)}{\pi rl}$

$=\frac{(r+l)}{l}$
$=1+\frac{r}{l}=\frac{8}{5}$
$\Rightarrow \frac{r}{l}=\frac{3}{5}$

From the relation
$l^2=h^2+r^2$,

$(\frac{l}{r}{)}^2=(\frac{h}{r}{)}^2+1$
$\Rightarrow \frac{25}{9}=(\frac{h}{r}{)}^2+1$
$\Rightarrow \frac{16}{9}=(\frac{h}{r}{)}^2$
$\Rightarrow \frac{4}{3}=\frac{h}{r}$
$\Rightarrow \frac{3}{4}=\frac{r}{h}$