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 volumes and the ratio of their curved surfaces.​

Answer 1

Answer:

Ratio of volume = 20 :27

Ratio of curved surface are = 10 :9

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

CSA =rh/RH

=2x×5y/3x×3y

=10xy/9xy

=10/9

Answer 2

Given :-

• Ratio of Radii of two cylinders = 2:3

• Ratio of heights of two cylinders = 5:3

To Find :-

• Ratio of volumes and Ratio of their curved surfaces.

Solution :-

Let the radii be 2x and 3x.

Let the height be 5y and 3y.

Now,

$:\implies\:\sf{Ratio\:of\:volume=\dfrac{r^2h}{12^2h} }$

$:\implies\:\sf{Ratio\:of\:volume=\dfrac{(2x^2)\times5y}{(3x^2)\times3y} }$

$\sf:\implies \underline{\boxed{\pink{\mathfrak{Ratio\:of\:volume=\dfrac{20}{27}}}}}\:\:\:\bigstar$

Ratio of curved surface area (CSA),

$:\implies\:\sf{\dfrac{r\times h}{R\times H} }$

$:\implies\:\sf{\dfrac{2x\times 5y}{3x\times 3y} }$

$:\implies\:\sf{\dfrac{10xy}{9xy} }$

$\sf:\implies \underline{\boxed{\pink{\mathfrak{\dfrac{10}{9}}}}}\:\:\:\bigstar$

$\displaystyle\therefore\:\underline{\textsf{Ratio of volume =\textbf{ 20:27}}}\\\\\displaystyle\therefore\:\underline{\textsf{Ratio of CSA =\textbf{ 10:9}}}$