Question

the ratio of curved surface area in the total surface area of right circular cylinder is 5:7 find the ratio between the height and the radius of the cylinder​

Answer 1

$\bold{\huge{\underline{\underline{\rm{ Given : }}}}}$

The ratio of curved surface and total surface area of right circular cylinder is 5 : 7

$\bold{\huge{\underline{\underline{\rm{To \: Find :}}}}}$

The ratio between the height and the radius of the cylinder.

$\bold{\huge{\underline{\underline{\rm{we \: know \: that :}}}}}$

$⟼\text{CSA} = 2\pi \text{rh}$

$⟼ \text{TSA} = 2\pi \text{r}( \text{r} + \text{h})$

$\bold{\huge{\underline{\underline{\rm{Solution \: :}}}}}$

$: ⟹\frac{ \text{ratio of curved surface area}}{ \text{ratio of total surface area}} = \frac{5}{7}$

$: ⟹ \frac{2\pi \text{rh}}{2\pi \text{r}} ( \text{r + h} ) = \frac{5}{7}$

$: ⟹ \frac{ \text{ {{h }}}}{ \text{{r + h}}} = \frac{5}{7}$

$: ⟹7 \text{h} = (\text{5r + 5h})$

$: ⟹ \text{7h - 5h = 5r}$

$: ⟹ \text{5h = 5r}$

$: ⟹ \frac{ \text{h}}{ \text{r}} = \frac{5}{2}$

$:⟹ \text{h : r} = 5 :2$

Hence, The ratio between the height and radius of cylinder is 5 : 2