Question

The radius of the base and height of cylinder are in 2:3
if the volume of cylinder is 16 17 cm ² calculate its total surface area ​

Answer 1

$\huge\green{Question}$⇒The radius of the base and height of cylinder are in 2:3

if the volume of cylinder is 16 17 cm ² calculate its total surface area ​

$\huge\red{answer}$⇒Consider radius as 2x cm and height as 3x cm

We know that

Volume of cylinder =πr²h

By substituting the values

Volume of cylinder =  22 /7 ×(2x)²×3x

On further calculation

Volume of cylinder =  22 /7 ×4x²  ×3x

So we get

Volume of cylinder =  22 /7 ×12x³

 It can be written as

1617=  22 /7 ×12x³

 On further calculation

12x³ =  1617×7 /22

So we get

x³=  1617×7/ 22×12

​x³ =42.875

By taking cube root

x=  ∛42.865

​x=3.5

By substituting the value of x

Radius =2x=2(3.5)=7cm

Height =3x=3(3.5)=10.5cm

We know that  

 Total surface area =2 πr(h+r)

By substituting the values

Total surface area =2×  22/ 7 ×7(10.5+7)

On further calculation

Total surface area =44×17.5

So we get

Total surface area =770 cm²

Therefore, the total surface area of the cylinder is 770 cm²

$\huge\pink{@alurringbabe}$

Answer 2

$\Large{\underbrace{\sf{\red{Required\:Answer:}}}}$

Given :

• The rαdius of the bαse and height of cylinder αre in 2:3.
• The volume of the cylinder is 1617cm².

To Find :

• Totαl surfαce αreα of th cylinder.

Required Knowledge :

$\large\star{\boxed{\sf{\red{ Volume_{(cylinder)} = (\pi)(radius)^{2}(height) = \pi r^{2}h}}}}$

$\large\star{\boxed{\sf{\red{ T.S.A_{(cylinder)} = 2\pi r(r+h) = 2\pi (radius) \big[ (radius)+(height)\big]}}}}$

Solution :

Let the rαdius of the bαse αnd height of the cylinder be 2x αnd 3x.

• Substitute the vαlues in the formulαe of the volume of cylinder.

$\longrightarrow{\sf{ 1617cm^{3} =\dfrac{22}{7} \times (2x)^{2}\times (3x)}}$

$\longrightarrow{\sf{ 1617cm^{3} = \dfrac{22}{7} \times 4x^{2} \times 3x}}$

$\longrightarrow{\sf{ 1617cm^{3} = \dfrac{22\times 4x^{2}\times 3x}{7}}}$

$\longrightarrow{\sf{ 1617 = \dfrac{264x^{3}}{7}}}$

$\longrightarrow{\sf{ x^{3} =\dfrac{1617\times 7}{1617}}}$

$\longrightarrow{\sf{ x^{3} = 42.875}}$

$\longrightarrow{\sf{ x =∛42.875}}$

$\longrightarrow{\sf{ x =3.5}}$

Therefore, the rαdius of the bαse is —

$\longrightarrow{\sf{ 2x = 2\times 3.5}}$

$\implies{\boxed{\sf{\red{ 7}}}}$

And the height of the cylinder is —

$\longrightarrow{\sf{ 3x = 3\times 3.5}}$

$\implies{\boxed{\sf{\red{ 10.5}}}}$

Now,

• Substitute the vαlues in the formulαe of T.S.A of cylinder.

$\longrightarrow{\sf{ 2\times \dfrac{22}{7}\times 7(7+10.5)}}$

$\longrightarrow{\sf{ 2\times \dfrac{22}{\cancel{7}}\times \cancel{7}\times (17.5)}}$

$\longrightarrow{\sf{ 44\times 17.5}}$

$\large\implies{\boxed{\sf{\red{ 770cm^{2}}}}}$

Hence, the totαl surfαce αreα of cylinder is 770cm².

And we αre done! :)

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