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 thickness and 15 cm long?
Answers
Answer:
Let The C1 is the smaller solid cylinder of height h₁.
radius = r₁ = diameter/2 = 2/2 = 1 cm.
now,
Volume of the C1 = V₁ = πr₁²h₁ = 3.14*(1)²h1 = 3.14.h₁
A/Q,
Solid Cylinder C₁ is recasted into a hollow Cylinder of height 15 cm.
diameter is 20 cm and its is 0.25 cm thick.
radius = r₂ = 20/2 = 10 cm.
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*15 [ 25² - (25-0.25)² ]
= 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*12.4375
= 585.80625
and,
The vol. of the small solid Cylinder C₁ = Vol. of the thick part of the Hollow cylinder.
⇒ 3.14h1 = 585.80625
h1 = 186.5625