Question

What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?

Answer 1

Let The C1 is the smaller solid cylinder of height h₁.
radius = r₁ = $\frac{diameter}{2}=1cm$
now,
Volume of the C1 = V₁ = πr₁²h₁ = 3.14.h₁
Solid Cylinder C₁ is recasted into a hollow Cylinder of height 15 cm.
diameter is 20 cm and it is 0.25 cm thick.
radius = r₂ = $\frac{20}{2}=10cm$
height = h₂ = 15 cm.
thickness = 0.25 cm.
Volume of thick part o hollow Cylinder = π(r₂)²h₂ - π(r₂ - 0.25)²h₂
= πh₂{r₂² - (r₂ - 0.25)²}

= $3.14\times 15[25²-(25-0.25\left)²\right]$

= 47.1[25² - (25² + 0.25² - 2*25*0.25)]

= 47.1( 25² -25² - 0.25² +2*25*0.25)

= 47.1( 12.5 - 0.0625)

= $47.1\times 12.4375$

= 585.80625


The vol. of the small solid Cylinder C₁ = Vol. of the thick part of the Hollow cylinder.

⇒ 3.14 h1 = 585.80625
h1 = 186.5625
Therefore the height of the small solid cylinder is 186.5625 cm.