Maths · Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions
A hollow spherical shell is made of metal of density If its internal and externa
A hollow spherical shell is made of metal of density \( 4.8 \mathrm{g} / \mathrm{cm}^{3} . \) If its internal and external radii are \( 10 \mathrm{cm} \) and \( 12 \mathrm{cm} \) respectively, find the weight of the shell
- A. \( 15.24 \mathrm{kg} \)
- B. \( 12.84 \mathrm{kg} \)
- C. \( 14.64 \mathrm{kg} \)
- D. None of these
Step-by-step solution
Volume of shell = (4/3)π(R^3 - r^3) = (4/3)π(12^3 - 10^3) = (4/3)π(1728 - 1000) = (4/3)π(728) = (2912/3)π cm^3. Mass = volume × density = (2912/3)π × 4.8 = 2912 × 1.6π = 4659.2π g ≈ 4659.2 × 3.1416 ≈ 14636.6 g = 14.6366 kg ≈ 14.64 kg.