Question

The total surface area of a hollow cylinder which is open from both sides is 3575 cm2 area of base ring is 357.6 cm2 and height is 14cm.Find thickness of cylinder

Answer 1

Given, total surface area of cylinder = 3575 cm2

Area of the base ring = 357.5 cm2

and height = 14 cm 

Let R is the radius of the outer ring and r is the radius of the inner ring.

Now, area of the base ring = 357.5

=> πR2 - πr2 = 357.5

=> π(R2 - r2 ) = 357.5

=> R2 - r2 = 357.5/π

=> R2 - r2 = (357.5 * 7)/22

=> R2 - r2 = 16.25 * 7

=> R2 - r2 = 113.75

=> (R - r)*(R + r) = 113.75 ............1

Again, total surface area = inner and outer curved surface area and area of the bottom and top rings 

=> 2πRh + 2πrh + 2 * 357.5 = 3575

=> 2πh(R + r) + 715 = 3575

=> 2πh(R + r) = 3575 - 715

=> 2πh(R + r) = 2860

=> R + r = 2860/2πh

=> R + r = 1430/πh

=> R + r = 1430/(22/7 * 2)

=> R + r = 715/(22/7)

=> R + r = (715 * 7)/22

=> R + r = 5005/22 ............2

From equation 1, we get

     (R - r) * 5005/22 = 113.75

=> R - r = (113.75 * 22)/5005

=> R - r = 2502.5/5005

=> R - r = 0.5

So, the thickness of the cylinder = R - r = 0.5 cm