Math, asked by BrainlyHelper, 1 year ago

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?

Answers

Answered by nikitasingh79
23

Answer:

The length of a solid cylinder is 79 cm .

Step-by-step explanation:

SOLUTION :

Given :  

Let 'H’ be length of a solid cylinder.

Diameter of the solid cylinder, D = 2 cm

Length of the hollow cylinder, h = 16 cm

External diameter of the hollow cylinder, d1  = 20 cm  

Thickness of the hollow cylinder = 2.5 mm = 0.25 cm  

Radius of the Solid cylinder , R = 2/2 = 1 cm

External radius of the hollow cylinder, r1 = 20/2 = 10 cm

Internal radius of the hollow cylinder , r2 = External radius of the hollow cylinder - Thickness  

Internal radius of the hollow cylinder, r2  = 10 - 0.25 = 9.75 cm

Volume of the hollow cylinder  = πh(r1² −r2²)

Since the solid cylinder is recast into a hollow cylinder, so  

Volume of solid cylinder = Volume of hollow cylinder  

πR²H = πh(r1² −r2²)

R²H = 16(10² - 9.75²)

1²H = 16(100 - 95.0625)

H = 16 × 4.9375

H = 79 cm .

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

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Answered by Kusumsahu7
6

Given diameter of solid cylinder = 2 cm

Radius of solid cylinder,

r = 1 cm

 Volume of solid cylinder =  πr2h = π × 12 × h = πh → (1) Length of hollow cylinder,

H = 16 cm

External diameter = 20 cm 

External radius = 10 cm

 Thickness = 2.5 mm = 0.25 cm

Internal radius = 10 – 0.25 = 9.75 cm

Volume of hollow cylinder  = π[102 – (9.75)2] × 16 = 16π × 19.75 × 0.25 →  (2)From (1) and (2), we get Πh = 16π × 19.75 × 0.25  

 ∴ h = 16 × 19.75 × 0.25 = 79 cm 

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