Question

The radii 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.
war diameter of a gas cylinder is 20 cm. Find them
TL​

Answer 1

Answer:

The radii of two cylinder are in the ratio of 2:3

so , Radius of first cylinder is 2r

And , Radius of second cylinder is 3r

Height are in the ratio of 5:3 .

Then , Height of 1st cylinder = 5h

or Height of 2nd cylinder = 3h

Ratio of volume = volume of 1st cylinder/ volume of 2nd cylinder

V = π(2r)^2 × 5h / π(3r)^2 × 3h

V = 20rh / 27 rh

v = 20/ 27 .

The volume of cylinder is 20/27 is also known as the total surface area of the cylinder ( hollow ) .

Note :- TSA / V = πr^2 × hr^2 × h .

Answer 2

$\\ \\\underline{\large \sf \: Correct \: Question :-}$

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5:3. Calculate

$\\ \\\underline{\large \sf \: Given \: :-}$

$\\ \bigstar \: \rm \: Ratio \: of\: radii\: of\: two\: cylinder\: = 2 : 3$

$\\ \bigstar \: \rm \: Ratio \: of\: height\: of\: two\: cylinder\: = 5: 3$

$\\ \\\underline{\large \sf \: To \: find \: :-}$

$\\ \rm \: (i) \: Ratio \: of \: the \:curved \: surface \: area \: \: of \: the \: two \: cylinders \:$

$\\ \\\underline{\large \sf \: Solution \: :-}$

$\\ \\ \rm \: Let \: r_1 \: and \: r_2 \: b e \: the \: radii \: of \: the \: \\ \rm cylinders\: respectively \: .$

$\\ \\ \rm \: Let \: h_1 \: and \: h_2 \: b e \: the \: height\: of \: the \: \\ \rm cylinders\: respectively \: .$

$\\ \\ \sf \: \: \: \: \: \: \: Therefore, \: we \: have$

$\\ \\ \rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac {r_1} {r_2} \: = \frac{2}{3}$

$\\ \\ \rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac {h_1} {h_2} \: = \frac{5}{3}$

$\\ \\ \rm \: Since ,\: we \: have\: to \: find \: the \: ratio \: of \: curved \: surface \\ \rm \: area \: of \: two \: cylinder . \: we \: have,$

$\\ \\ \: \: \: \: \: \: \: \rm \frac{ \: Curved \: surface \: area \: of \: cylinde \: 1}{ \: Curved \: surface \: area \: of \: cylinde \: 2} \: = \: \frac{2\pi r_1h_1 }{2\pi r_2h_2}$

$\\ \\ \rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \: \bigg(\frac{r_1 }{r_2} \bigg) \bigg(\frac{h_1}{h_2} \bigg)$

$\\ \\ \rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \: \bigg(\frac{2}{3} \bigg) \: \bigg(\frac{5}{3} \bigg)$

$\\ \\ \: \: \: \: \: \: \: \underline{\boxed{\tt \frac{ \: Curved \: surface \: area \: of \: cylinde \: 1}{ \tt\: Curved \: surface \: area \: of \: cylinde \: 2} \: = \: \bigg(\frac{10 }{9} \bigg)} }$

$\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \: \: \bf{the \: ratio \: of \: their \: curved \: surface \: areas \: is \: \frac{10}{9} \: .}}$