The difference between the outer and inner curved surface areas of a hollow right circular cylinder 14 cm long is 88 cm 2 . If the volume of metal used in making the cylinder is 176 cm 3 , find the outer and inner diameters of the cylinder.

Question

Philoid · Accepted Answer

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 = 88

⇒ R – r = 1 ……… (1)

Volume of metal = 176

Height of hollow cylinder = 14 cm

Volume of hollow cylinder (metal) =

⇒ (R + r)(R – r) = 4

⇒ (R + r) = 4 ………… (2)

Solving (1) and (2) we get,

R = 2.5cm

r = 1.5cm

∴ Outer diameter cm

= 5 cm

Inner diameter cm

= 3 cm

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.

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.