Question

The ratio of the heights of two cylinders is 5:3 and the ratio of their radii is
2:3. Find the ratio of the volumes of these cylinders.​

Answer 1

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Answer 2

AnswEr:

GivEn:

• Ratio of Height (Cylinders) = 5:3
• Ratio of Radius ( Cylinders) = 2:3

To Find:

• Ratio of the Volumes ( Cylinders) - ?

Solution:

Let the the heights of cylinders be h1 , h2 and

Radius be r1 , r2 ;

Equation 1st:

${\sf{ \dfrac{r_{1}}{r_{2}} = \dfrac{2}{3} \: \: \: \: ...(i) }} \\ \\ \sf{and,}$

Equation 2nd:

${\sf{ \dfrac{h_{1}}{h_{2}} = \dfrac{5}{3} \: \: \: \: ...(ii) }}$

Ratio of the volume of the both cylinders,

$\\ \huge\purple{\boxed{\sf{ \frac{V_{1}}{V_{2}} = \frac{πr^2_{1}h_{1}}{πr^2_{2}h_{2}} }}} \\ \\ \implies{\sf{ ( \dfrac{r_{1}}{r_{2}} )^2 \times \dfrac{h_{1}}{h_{2}} }} \\ \\ \implies{\sf{ ( \dfrac{2}{3} )^2 \times \dfrac{5}{3} }} \\ \\ \implies {\sf{ \dfrac{4}{9} \times \dfrac{5}{3} }} \\ \\ \implies\red{\boxed{\sf{ \dfrac{20}{27} }}}$

Hence,

The Ratio of the Volumes of cylinders is 20:27.