Question

The difference between the outer and inner curved surface areas of a hollow right circular cylinder 14 cm long is 88 cm². If the volume of metal used in making the cylinder is 176 cm³, find the outer and inner diameters of the cylinder.[ use π = \(\frac{22}7\)].

Answer 1

Height of hollow cylinder =14 cm 

Let the radius of outer radius be ‘R’ cm 

Let the radius of inner radius be ‘r’ cm 

Difference between inner and outer Curved surface area = 88 cm 

Curved surface area of hollow cylinder = 2π(R - r)h

⇒ 2π(R – r)h = 88 

⇒ R - r = \(\frac{{88}\times{7}}{{2}\times{22}\times{14}}\)

⇒ R – r = 1 ……… (1) 

Volume of metal = 176 

Height of hollow cylinder = 14 cm 

Volume of hollow cylinder (metal) =π(R² - r²)h