Question

What length of a solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm?

Answer 1

Given,

Length of solid cylinder = L

diameter of cylinder = 2 cm

radius of cylinder = \(\frac{2}{2}\) = 1 cm

Volume of cylinder = πr²L..............(i)

Length of hollow cylinder = 16 cm

External diameter = 20 cm

External radius = \(\frac{20}{2}\) = 10 cm

thickness = 2.5 mm = 0.25 cm

so,

inner radius = 10 - 0.25 = 9.75 cm

Volume = π(R² - r²)L = π(10² - 9.75²) x 16 ... . .. . .(ii)

From (i) and (ii)

= π x 1 x 1 x L = π(10² - 9.75²) x 16 

= L =79 cm