Question

The difference between outer and inner curved surface areas of a hollow right circular cylinder 14cm long is 88cm². If the volume of metal used in making cylinder is 176cm³.find the outer and inner diameters of the cylinder____?

Answer 1

Given height of a hollow cylinder = 4cm

Let internal and external radii of hollow

Cylinder be ‘r’ and R

Given that difference between inner and outer

Curved surface = 88cm²

Curved surface area of cylinder (hollow)

= 2π (R - r)h cm²

⇒ 88 = 2π(R - r)h

⇒ 88 = 2π(R - r)14

⇒ R - r = 1             ...........(1)

Volume of cylinder (hollow) = π(R² - r²)h cm²

Given volume of a cylinder = 176cm³

⇒ π(R² - r²)h = 176

⇒ π(R² - r²) x 14 = 176

⇒ R² - r^{2 = 4}

⇒ (R + r)(R - r) = 4

⇒ R + r = 4             .................(2)

    R - r = 1

+  R + r = 4 

    2R    = 5

2R = 5 ⇒ R = 5/2 = 2.5cm

Substituting ‘R’ value in (1)

⇒ R - r = 1

⇒ 2.5 - r = 1

⇒ 2.5 - 1 = r

⇒ r = 1.5cm

∴Internal radii of hollow cylinder = 1.5cm

External radii of hollow cylinder = 2.5cm