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 curved surface areas.​

Answer 1

$\large{ \textsf{\textbf {\pink {➽ \: \: Answer \: :-}}}}$

Let the radii be 2x and 3x,

let the height be 5y and 3y.

so, ratio of volume =r²h/R²H =(2x)²×5y/(3x)²×3y =20x²y/27x²y =20/27,

ratio of CSA =rh/RH =2x×5y/3x×3y =10xy/9xy =10/9.

the value of x and y can be termed to be get highes value and therefore bring forth in taking radius calculation

Answer 2

What we have to do ?

We have given two cylinders width ratio of radii be 2:3 and ratio of their height be 5 : 3 respectively. First we consider the radii and heights be in terms of variable and thereafter we will apply the formula for finding curve surface area and then we will find the ratio of their CSA.

Ratio of their radii → 2 : 3

• Let we consider the radii of first Cylinder be 2r

• Radii of second cylinder be 3r

Ratio of their heights → 5 : 3

• Let we consider the height of first cylinder be 5h

• Radii of second cylinder be 3h

Now,

Formula need to know :

${\boxed{\bf{Curved \: surface \: of \: cylinder = 2 \times \pi r \times h}}}$

Now,

For CSA of First cylinder :-

$\dashrightarrow\:\:\sf Curved \: surface \: of \: cylinder = 2 \times \pi \times r \times h$

Substituting the respective values, we get :

$\dashrightarrow\:\:\sf Curved \: surface \: of \: cylinder = 2 \times \pi \times 2r \times 5h$

$\dashrightarrow\:\:\sf Curved \: surface \: of \: cylinder = 2 \times \pi \times 10rh$

$\dashrightarrow\:\:\sf Curved \: surface \: of \: cylinder = 20rh \times \pi$

$\dashrightarrow\:\:\sf Curved \: surface \: of \: cylinder = 20 \pi rh$

Now, For Second Cylinder :-

$:\implies \sf Curved \: surface \: of \: cylinder = 2 \times \pi \times r \times h$

Substituting the respective values, we get :

$:\implies \sf Curved \: surface \: of \: cylinder = 2 \times \pi \times 3r \times 3h$

$:\implies \sf Curved \: surface \: of \: cylinder = 2 \times \pi \times 9rh$

$:\implies \sf Curved \: surface \: of \: cylinder = 18rh \times \pi$

$:\implies \sf Curved \: surface \: of \: cylinder = 18 \pi rh$

Ratio of their CSA :-

Substituting the respective values, we get :

$\dashrightarrow\:\:\sf Ratio = \dfrac{Curved \: surface \: of \: cylinder \: 1}{Curved \: surface \: of \: cylinder \: 2}$

$\dashrightarrow\:\:\sf Ratio = \dfrac{20 \pi rh}{18 \pi rh}$

$\dashrightarrow\:\:\sf Ratio = \dfrac{20}{18}$

$\sf \longrightarrow \: Ratio \: = {\dfrac{ \cancel{20}^{ \: \: 10} }{ \cancel{18}^{ \: \: 9} } \:}$

$\dashrightarrow\:\:\sf Ratio = \dfrac{10}{9}$

Hence,

$\dashrightarrow\:\: \underline{ \boxed{\sf Ratio \: of \: their \: CSA \: = 10: 9 }}$

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