The total surface area of a hollow cylinder which is open from both si

1.	The total surface area of a hollow cylinder which is open from both sides if 4620 sq. cm, area of base ring is 115.5 sq. cm. and height 7 cm. Find the thickness of the cylinder.
Answer» We have, Total surface area of hollow cylinder = 4620 cm² Area of base ring = 115.5 cm² Height of cylinder = 7 cm Let outer radius be ‘R’ cm , inner radius be ‘r’ cm Area of hollow cylinder = 2π(R² – r²) + 2πRh + 2πrh = 2π(R+r)(R-r) + 2πh(R+r) = 2π(R+r) (h+R-r) Area of base = πR² – πr² = π (R² – r²) = π (R+r) (R-r) Surface area / area of base = 4620/115.5 {2π(R+r) (h+R-r)} / { π (R+r) (R-r)} = 4620/115.5 2(h+R-r) / (R-r) = 4620/115.5 Let us consider (R-r) = t 2(h+t)/t = 40 2h + 2t = 40t 2h = 38t 2(7) = 38t 14 = 38t t = 14/38 = 7/19 cm ∴ Thickness of cylinder is 7/19 cm.

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

Answer»

We have,

Total surface area of hollow cylinder = 4620 cm²

Area of base ring = 115.5 cm²

Height of cylinder = 7 cm

Let outer radius be ‘R’ cm , inner radius be ‘r’ cm

Area of hollow cylinder = 2π(R² – r²) + 2πRh + 2πrh

= 2π(R+r)(R-r) + 2πh(R+r)

= 2π(R+r) (h+R-r)

Area of base = πR² – πr²

= π (R² – r²)

= π (R+r) (R-r)

Surface area / area of base = 4620/115.5

{2π(R+r) (h+R-r)} / { π (R+r) (R-r)} = 4620/115.5

2(h+R-r) / (R-r) = 4620/115.5

Let us consider (R-r) = t

2(h+t)/t = 40

2h + 2t = 40t

2h = 38t

2(7) = 38t

14 = 38t

t = 14/38

= 7/19 cm

∴ Thickness of cylinder is 7/19 cm.