Question

If the ratio of curved surface area and total surface area of a cylinder is 1 : 4, find the ratio of radius and height of the cylinder.

• A. 1 : 4
• B. 3 : 1
• C. 2 : 3
• D. 2 : 5

Answer 1

The correct option is B 3 : 1

Given: CSA : TSA = 1 : 4

Curved surface area of cylinder = $2\pi rh$
Total surface area of cylinder = $2\pi r(h+r)$

$\frac{Curvedsurfacearea}{Totalsurfacearea}$ = $\frac{2\pi rh}{2\pi r(h+r)}$

$\frac{1}{4}$ = ​​​​​​​$\frac{2\pi rh}{2\pi r(h+r)}$

​​​​​​​$\frac{1}{4}$ = ​​​​​​​$\frac{h}{(h+r)}$
4h = h + r
3h = r
​​​​​​​$\frac{h}{r}$ = ​​​​​​​$\frac{1}{3}$
​​​​​​​$\frac{r}{h}$ = ​​​​​​​$\frac{3}{1}$
​​​​​​​r : h = 3 : 1