Question

7. The radii of two cylinders are in the ratio of 3 : 2
and their heights are in the ratio of 7:4. Find the
ratios of their curved surface areas.​

Answer 1

$\rm{ 21:8}$

Step-by-step explanation:

★Question -

• The radii of two cylinders are in the ratio of 3:2 and their heights are in the ratio of 7:4. Find the ratios of their curved surface areas.

★Given -

• Radii of two cylinders are in the ratio 3:2 .
• Heights of two cylinders are in the ratio 7:4 .

★To find -

• Ratio of their curved surface areas.

★Solution -

Let the radii of the two cylinders be 3x and 2x.

Let the heights of the two cylinders be 7y and 4y.

Cylinder (1)

Radius(R)= 3x

Height(H) = 7y

Cylinder (2)

Radius(r) = 2x

Height(h) = 4y

$\pink{\rm{ \dfrac{Curved \: surface \: area \: of \: cylinder(1)}{{Curved \: surface \: area \: of \: cylinder(2)}}} = \dfrac{ {2\pi} \: {RH}}{ {2\pi} \: {rh}} }$

$\boxed{\longmapsto\rm{ \dfrac{Curved \: surface \: area \: of \: cylinder(1)}{{Curved \: surface \: area \: of \: cylinder(2)}}} = \dfrac{ \cancel{2\pi} \: {RH}}{ \cancel{2\pi} \: {rh}}}$

$\boxed{ \longmapsto \rm{ \dfrac{Curved \: surface \: area \: of \: cylinder(1)}{{Curved \: surface \: area \: of \: cylinder(2)}}} = \dfrac{ {RH}}{ {rh}} }$

$\boxed{ \longmapsto \rm{ \dfrac{Curved \: surface \: area \: of \: cylinder(1)}{{Curved \: surface \: area \: of \: cylinder(2)}}} = \dfrac{ {3 \cancel{x }\: \times \: 7 \cancel{y}}}{ {2 \cancel{x }\: \times \: 4 \cancel{y}}} }$

$\boxed{ \longmapsto \rm{ \dfrac{Curved \: surface \: area \: of \: cylinder(1)}{{Curved \: surface \: area \: of \: cylinder(2)}}} = \dfrac{ {3 { }\: \times \: 7 {}}}{ {2 {}\: \times \: 4 {}}} }$

$\boxed{ \longmapsto \rm{ \dfrac{Curved \: surface \: area \: of \: cylinder(1)}{{Curved \: surface \: area \: of \: cylinder(2)}}} = \dfrac{ {21 {}}}{ {{8}}} }$

$\blue{ \rm{Therefore, the \: ratio \: is \: 21:8}}$