Question

Thw total surface area of a hollow cylinder,which is open from the sides ,is 3575cm2,the area of its basering is 357.5cm2 and its height is 14cm .find the thickness of the cylinder

Answer 1

Total surface of hollow cylinder is summation of area of its internal surface, outer surface and its both end base.
Let us assume r and R are inner and outer diameter of hollow ring, and h is height
Total surface area (S) = outer surface area + inner surface area + 2 * base area
S = 2π Rh + 2π rh + 2*π(R²-r²)
S = 2π(R+r)(h+R-r)
From the given total surface area (in cm²),
2π(R+r)(h+R-r) = 3575....................(i)
Area of base ring, A = π (R²-r²) = 357.5........................(ii)
Dividing equation, (i)/(ii)
[2π(R+r)(h+R-r)]/[π (R²-r²)] = 3575/357.5
2(h+R-r)/(R-r) = 10
h+R-r = 5 (R-r)
Putting value of h = 14
14 + (R-r) = 5(R-r)
14 = 4(R-r)
R-r = 14/4 = 3.5
Thickness of hollow cylinder is (R-r) which comes out to be 3.5 cm

Answer = 3.5cm