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 The total surface area of a hollow cylinder which is open from both sides is 4620 sq.cm,area of base ring is 115.5sq.cm and height 7cm. Find the thickness of the cylinder.

 Let R be the external radius of cylinder and r be the internal radius of cylinder.

Then = 2*pie*R*h + 2*pie*r*h + 2 * pie ( R2 - r2) = 4620

pie ( R2 - r2) = 115.5

By substituting pie * ( R2 - r2 ) = 115.5 in first equation , we will get

2*pie*R*h + 2*pie*r*h  + 2* 115.5 = 4620

2*pie*R*h + 2*pie*r*h  + 231 = 4620

2*pie*R*h + 2*pie*r*h  = 4620 - 231 = 4389

Now taking 2 * pie * h as common we get

2 * pie * h ( R + r) = 4389

2 * (22 / 7) * 7  ( R + r) = 4389

44(R + r) =  4389

(R + r ) = 4389 / 44 by cutting it by eleven we get 399 / 4

We nknow that 

pie * (R2 - r2) = 115.5 which implies

(22 / 7) * (R - r) ( R + r) =  115.5

R + r = 399 / 4

(22 / 7) * (399 / 4) * (R - r) = 115.5

R - r = (115.5 * 7  * 4) / ( 22 * 399)

R - r = 7 / 9 cm

See R - r is always the thickness please remember.

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 ANS: Given: Total surface area of cylinder = 4620 cm2

                       Area of base ring = 115.5cm2

                       Height = 7cm 

Let R be the radius of outer ring and r be the radius of the inner ring 

Area of base ring =  πR2 -  πr2  = π(R2- r2) = 115.5 cm2

=> R2- r2   = 115.5*7/22  cm2 

= 36.75

= > (R + r )(R-r) =  36.75   ....... Equation(1)

4620=2πRh + 2πrh + 2* 115.5   [Since total surface area = inner and outer curved surface area and area of bottom and top rings]

2πh (R + r) = 4620- 231

R+r = (4389*7)/(2*22*7)= 399/4

R+r= 399/4          .......Equation (2)

Substituting the value of   R+r  from equation (2) in equation (1)

= >399/4(R-r) =  36.75

=> (R- r) =  36.75*4/399 = 0.368cm 

Therfore the thicknes of the cylinder = (R- r) = 0.368cm

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Given: Total surface area of cylinder = 4620 cm2

Area of base ring = 115.5cm2

Height = 7cm

Let R be the radius of outer ring and r be the radius of the inner ring

Area of base ring = πR2 - πr2 = π(R2- r2) = 115.5 cm2

=> R2- r2 = 115.5*7/22 cm2

= 36.75

= > (R + r )(R-r) = 36.75 ....... Equation(1)

4620=2πRh + 2πrh + 2* 115.5 [Since total surface area = inner and outer curved surface area and area of bottom and top rings]

2πh (R + r) = 4620- 231

R+r = (4389*7)/(2*22*7)= 399/4

R+r= 399/4 .......Equation (2)

Substituting the value of R+r from equation (2) in equation (1)

= >399/4(R-r) = 36.75

=> (R- r) = 36.75*4/399 = 0.368cm

Therfore the thicknes of the cylinder = (R- r) = 0.368cm

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Dear Student!

@all: Very good! Keep posting!

verma.kriti111 check the expression for R – r in the end of the solution.

Cheers!

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