Question

The radil of two cylinders are in the ratio 2:3 and their heights are in the ratio
5:3. Calculate the ratio of their curved surface areas.​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• Radii of two cylinders = 2:3

• Height of two cylinders = 5:3

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• Ratio of their curved surface areas

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Let the radius of cylinder be r₁ and r₂.

The height of the cylinder be h₁ and h₂.

$\underline{\:\textsf{ As we know that :}}$

• Curved surface area of cylinder = 2πrh

Then,

$\tt{ \longrightarrow \dfrac{r_{1}}{r_{2}} = \dfrac{2}{3} }$

$\tt{ \longrightarrow \dfrac{h_{1}}{h_{2}} = \dfrac{5}{3} }$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\:\textsf{ Now , find the ratio of their curved surface areas. :}}$

$\tt{\longrightarrow \dfrac{\cancel{2\pi} r_1 h_1 }{\cancel{2\pi} r_2 h_2 } }$

$\tt{\longrightarrow \dfrac{r_{1}}{r_{2}} \times \dfrac{h_{1}}{h_{2}} }$

$\tt{ \longrightarrow \dfrac{2}{3} \times \dfrac{5}{3} }$

$\tt{ \longrightarrow \dfrac{10}{9} }$

$\bf{ \longrightarrow 10:9}$

$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{The ratio of their curved surface areas is \textbf{ 10:9 }}}.$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\;\;\underline{\textbf{\textsf{ Know More:-}}}$

•Volume of cylinder = πr²h

•T.S.A of cylinder = 2πrh + 2πr²

•Volume of cone = ⅓ πr²h

•C.S.A of cone = πrl

•T.S.A of cone = πrl + πr²

•Volume of cuboid = l × b × h

•C.S.A of cuboid = 2(l + b)h

•T.S.A of cuboid = 2(lb + bh + lh)

•C.S.A of cube = 4a²

•T.S.A of cube = 6a²

•Volume of cube = a³

•Volume of sphere = 4/3πr³

•Surface area of sphere = 4πr²

•Volume of hemisphere = ⅔ πr³

•C.S.A of hemisphere = 2πr²

•T.S.A of hemisphere = 3πr²

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

$\sf \: \large cylinder = 1$
$\sf \large \: radil = r_1$
$\sf \large \: height = h_1$

$\sf \large \: cylinder = 2$
$\sf \large \: radi \: = r_2$
$\sf \large \: height = h_2$

$\sf \large \frac{r_1}{r_2} = \frac{2}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{h_1}{h_2} = \frac{ - 5}{3}$

$\large \color{red} \sf \: curved \: surface \: area = 2 \pi \: rh$

$\color{blue} \sf \large \: s - 1 = 2 \pi \: r_1 \: h_1$

$\sf \color{orange} \large \: s - 2 = 2\pi \: r_2 \: h_2$

$\pink {\sf \large \: \frac{s - 1}{s - 2} = \frac{2 \pi \: r_1 \: h_1}{2 \pi \: r_2 \: h_2} = \bigg( \frac{r_1}{r_2 } \bigg) \bigg( \frac{h_1}{h_2} \bigg)}$

$\color{lime} = \sf \large \frac{2}{3} \times \frac{5}{3} = \frac{10}{9} = 10 \ratio \: 9$