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
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 .
HOPE THIS ANSWER WILL HELP YOU...
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