Question

If two cylinders of same curved surface area have their radii in the ratio 4 : 9, then the ratio of their heights is

Answer 1

Answer:

The ratio of their heights is 9 : 4

Step-by-step explanation:

Here,

Curved surface area of both cylinders are same

$2\pi \: r1 \: h1 = 2\pi \: r2 \: h2$

:. 2 and pi will be cancel.

$r1 \: h1 = r2 \: h2$

$\frac{r1}{r2} = \frac{h2}{h1}$

$\frac{4}{9} = \frac{h2}{h1}$

Therefore, h1 : h2 = 9 : 4

Hope it will help you ..

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{h_{1}:h_{2}=9:4}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies C.S.A \: of \: cylinder \: first = C.S.A\: of \: cylinder \: 2 \\ \\ \tt: \implies Ratio \: of \: Radii = 4 : 9 \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Ratio \: of \: their \: Heights = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Ratio \: of \:C.S.A= \frac{C.S.A\: of \: first \: cylinder}{C.S.A \: of \: second \: cylinder } \\ \\ \tt: \implies \frac{2\pi \: r_{1}h_{1} }{2\pi \: r_{2} h_{2} } = 1 \\ \\ \tt: \implies \frac{4 \times h_{1}}{9 \times h_{2} } = 1 \\ \\ \tt: \implies \frac{h_{1}}{h_{2} } = \frac{9}{4} \\ \\ \green{\tt: \implies h_{1} : h_{2} = 9 : 4} \\ \\ \purple{\tt{Some \: related \: formula \: to \: this \: topic}} \\ \pink{ \tt\circ \: T.S.A \: of \: cylinder = 2\pi r(h + r)} \\ \\ \pink{ \tt\circ \: Volume\: of \: cylinder =\pi {r}^{2}h }$