Question

The rade of two cylindey are in the ratio of 4:5
and their
their heights
are in the ratio
of 7:6 find the
ratio of their
lateral
Surface areas.
of
uis​

Answer 1

Appropriate Question:

The radii of two cylinders are in the ratio of 4 : 5 and their heights are in the ratio of 7 : 6. Find the ratio of their L.S.A.

Required Solution:

Let ,

• Radius of the first cylinder (r) = 4x
• Radius of the second cylinder (R) = 5x

Also,

• Height of the the first cylinder (h) = 7x
• Height of the second cylinder (H) = 6x

We know that,

$\longmapsto \boxed { \bf { {L.S.A}_{(Cylinder)} = 2\pi r h }}$

So, according to the question :

$\longrightarrow \sf { Ratio = \dfrac{ {L.S.A}_{(1st \: Cylinder)}}{ {L.S.A}_{(2nd \: Cylinder)}} }$

$\longrightarrow \sf {Ratio= \dfrac{2 \pi rh}{2 \pi RH} }$

Substituting values,

$\longrightarrow \sf {Ratio= \dfrac{2 \times \cancel{\pi} \times 4x \times 7x }{2 \times \cancel{ \pi } \times 5x \times 6x } }$

$\longrightarrow \sf {Ratio= \dfrac{2 \times 28\cancel{{x}^{2}} }{2 \times 30 \cancel{{x}^{2}} } }$

$\longrightarrow \sf {Ratio= \dfrac{\cancel{2} \times 28 }{\cancel{2} \times 30 } }$

$\longrightarrow \sf {Ratio= \dfrac{28 }{30 } }$

$\longrightarrow \sf {Ratio= \dfrac{14}{15 } }$

$\longrightarrow \sf \red {Ratio= 14:15 }$

Henceforth,

• Ratio of their lateral surface areas is 14:15.

⠀⠀⠀⠀⠀_____________

More formulae!

$\longrightarrow$ Volume of cylinder = πr²h

$\longrightarrow$ L.S.A of cylinder = 2πrh

$\longrightarrow$ T.S.A of cylinder = 2πr (r + h)

Answer 2

Ratio of radii = 4:5

Ratio of heights = 7:6

We know,

LSA of a right circular cylinder = 2πrh

∴ Ratio of LSAs = (2πRH)/(2πrh)

⇒ Ratio of LSAs = (RH)/(rh)

⇒ Ratio of LSAs = (4 × 7)/(5 × 6)

⇒ Ratio of LSAs = 28/30 = 14/15

So, ratio of theirs LSAs is 14:15.