Question

The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volumes is *
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Answer 1

Step-by-step explanation:

As radii of two cylinder in in ratio of 2:3

So radius of 1st cylinder=2r

 radius of 2st cylinder=3r

heights are in the ratio 5:3. 

height of 1st cylinder=5h

height of 2st cylinder=3h

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

 V=Π(2r)2∗5h/Π(3r)2∗3h

V=20rh/27rh

V=20/27

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Answer 2

The Ratio of the volume of Cylinders is 20:27 .

Given:

• Radii = 2:3
• Height = 5:3

Explanation:

Let the heights be ${\sf{ h_1,h_2}}$ and Radii be ${\sf{ r_1,r_2}}$

• Radius of two Cylinders be 2 and 3

• Heights of two Cylinders be 5 and 3

So, Equations be like;

${\sf{ \dfrac{r_1}{r_2} = \dfrac{2}{3} \: \: \: \cdots (1) }} \\ \\ {\sf{ \dfrac{h_1}{h_2} = \dfrac{5}{3} \: \: \: \cdots (2) }}$

$\dag{\boxed{\underline{\sf{ Volume_{(Cylinder)} = πr^2h }}}}$

According to Question,

Let Volumes of Both Cylinders be ${\sf{ V_1,V_2} }$

$\colon\implies{\sf{ \dfrac{V_1}{V_2} = \dfrac{πr^2h}{πr^2h} }} \\ \\ \\ \colon\implies{\sf{ \dfrac{V_1}{V_2} = \dfrac{ \cancel{π} \ r^2h}{ \cancel{π} \ r^2h} }} \\ \\ \\ \colon\implies{\sf{ \dfrac{V_1}{V_2} = \dfrac{ (2)^2 \times 5}{ (3)^2 \times 3 } }} \\ \\ \\ \colon\implies{\sf{ \dfrac{V_1}{V_2} = \dfrac{ 4 \times 5}{9 \times 3 } }} \\ \\ \\ \colon\implies{\sf{ \dfrac{V_1}{V_2} = \dfrac{20}{27 } }} \\ \\ \\ \colon\implies{\boxed{\sf\pink{ 20 \colon 27 }}}$

Hence,

• The Ratio of two Cylinders is 20:27 .