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 millimetre ​

Answer 1

||✪✪ 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 millimetre ?

|| ★★ FORMULA USED ★★ ||

• Volume of Solid Cylinder = π * r² * h
• Volume of Hollow Cylinder = π * (R² - r²) * H
• Internal Radius of Hollow Cylinder = ( External Radius - Thickness) .
• when A solid is recast to form New Solid , than their Volume will be same .
• 1cm = 10mm.
• Radius = (Diameter /2)

|| ✰✰ ANSWER ✰✰ ||

→ Diameter of Solid Cylinder = 2cm.

→ Radius of Solid Cylinder = (2/2) = 1cm.

→ Height of Solid Cylinder = Let h cm.

Than,

→ Volume of Solid cylinder = π * r² * h = π * (1)² * h = π*h cm³ ------------ Equation (1)

______________________

Now,

→ Height of Hollow Cylinder = 16cm.

→ External Diameter = 20cm.

→ External Radius = R = (20/2) = 10cm.

→ Internal Radius = r = (10 - (2.5/10) ] = (10 - 0.25) = 9.75cm.

So,

→ Volume of Hollow Cylinder = π * 16 * [ (10)² - (9.75)²] = 16π * [ 100 - 95.0625] = (16π * 4.9375) cm³ ---- Equation (2) .

_______________________

Now, Since Volume of Both Will be same, So, Comparing Both Equations Now, we get,

→ π * h = 16 * π * 4.9375

π will be Cancel From both Sides,

→ h = (16 * 4.9375)

→ h = 79cm.

•°• Length of Solid Cylinder was 79cm.

Answer 2

Answer :-

79 cm

Solution :-

External diameter of the hollow cylinder = 20 cm

External radius of the hollow cylinder ( R ) = 20/2 = 10 cm

Thickness of the hollow cylinder = 2.5 mm = 2.5/10 cm = 0.25 cm

[ Since 1 cm = 1/10 mm ]

Inner radius of the hollow cylinder ( r ) = 10 - 0.28 = 9.75 cm

Length of the hollow cylinder i.e height ( h ) = 16 cm

Diameter of the solid cylinder = 2 cm

Radius of the solid cylinder ( r' ) = 2/2 = 1 cm

Let the length of the solid cylinder i.e height be h' cm

Given

Solid cylinder is recasted into a hollow cylinder

Therefore, Volume of solid cylinder = Volume of hollow cylinder

⇒ π * ( r' )² * h' = π * (R² - r²) * h

Cancelling π on both sides

⇒ ( r' )² * h' = (R + r)(R - r) * h

⇒ 1² * h' = (10 + 9.75)(10 - 9.75) * 16

⇒ 1 * h' = 19.75 * 0.25 * 16

⇒ h' = 4.9375 * 16

⇒ h' = 79

Hence, the length of the solid cylinder is 79 cm.