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 the solid cylinder is 79.04 cm.
Step-by-step explanation:
Solution↴
Given,
- Diameter of the solid cylinder = 2 cm
- Diameter of the solid cylinder = 2 cmLength of hollow cylinder = 16 cm
The solid cylinder is recast into a hollow cylinder of length 16 cm, external diameter of 20 cm and thickness of 2.5 mm = 0.25 cm
✔️We know that
✔️Volume of a cylinder = πr2h
✔️Radius of the solid cylinder = 1 cm
↪️So,
Volume of the solid cylinder = π12h = πh cm³
Let’s assume the length of the solid cylinder as h
And,
Volume of the hollow cylinder = πh(R²– r²)
Thickness of the cylinder = (R – r)
0.25 = 10 – r
So, the internal radius of the cylinder is 9.75 cm
Volume of the hollow cylinder = π × 16 (100 – 95.0625)
⏩Hence, it’s understood that
Volume of the solid cylinder = volume of the hollow cylinder
πh = π × 16(100 – 95.06)
↪️h = 79.04 cm
✔️Therefore, the length of the solid cylinder is 79.04 cm.
Answer:
The solid cylinder is recast into a hollow cylinder of length 16 cm, external diameter of 20 cm and thickness of 2.5 mm = 0.25 cm
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