Question

The difference between the outer and inner curved surface area of a hollow cylinder is 264 cm². If its height is 14 cm and the volume of the material in it is 1980 cm³, find its total surface area.

Answer 1

Curved surface area of cylinder = πr²h
Height h = 14cm
The difference between the outer and inner curved surface area = 264cm²
2π x {(R_outer)-(R_in)} x h = 264cm²
⇒ π x {(R_outer)-(R_in)} x h = 132     ...(1)
Volume of material in cylinder = 1980cm³
π{(R_outer)²-(R_in)²} x h = 1980
π{(R_ouer)-(R_in){(R_outer+(R_in)} x h = 1980   ...(2)
Substituting (1) in (2), we get
{(R_outer+(R_in)} x 132 = 1980
∴ {(R_outer+R_in)} = 15cm
Total surface area of a hollow cylinder
= 2π{(R_outer+R_in)} x h + 2π{(R_outer)²-(R_in)²}

= `2pi xx 15 xx 14 + 2 xx (1980)/(14)`
= 1602cm²
∴ The total surface area of the hollow cylinder is 1602cm².