22. The weight of a metallic spherical shell is 11.176 kg. If the inner radius of the shell is 6 cm, and
1 cm of the metal weighs 21 g then find the thickness of the shell.
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Given Parameters :
- Inner radius (r) = 6 cm
- Outer radius (R) = ?
- Density = 21 g/cm³
- Weight of metallic spherical shell = 11.176 kg = 11176 g
Answer:
→ Volume = Weight/Density
→ Volume = 11176/21
→ Volume = 532.19 cm³
→ So, Volume of material = 4/3 π (Outer Radius - Inner Radius)
→ Volume of material = 4/3 π (R³ - r³)
→ Volume of material = 4/3 π (R³ - 6³)
→ 532.19 = 4/3 π (R³ - 6³)
→ R³ - 6³ = (532.19 × 3 × 7)/4 × 22
→ R³ - 6³ = (532.19 × 3 × 7)/4 × 22
→ R³ - 6³ = 11175.99/88
→ R³ - 6³ = 126.99
→ R³ - 216 = 127
→ R³ = 127 + 216
→ R³ = 343
→ R = ∛343
→ R = 7 cm
Hence,Outer radius of is 7 cm.
____________________...
➝ Thickness = Outer radius - Inner radius
➝ Thickness = R - r
➝ Thickness = 7 - 6
➝ Thickness = 1 cm
Therefore,thickness of the shell is 1 cm.
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