A solid sphere of radius 4cm has a mass of 64kg. What will be the mass of a shell of the same metal whose internal and external radii are 2cm and 3cm respectively?
A. 5kg B. 16kg C. 19kg D. 6kg
Correct Answer: A
Explanation
\(\frac{1\sqrt{3}}{(\frac{1}{2})^2}\) = \(\frac{4}{\sqrt{3}}\) = \(\frac{\sqrt{3}}{\sqrt{3}}\) = \(\frac{4\sqrt{3}}{\sqrt{3}}\) m = 64kg, V = \(\frac{4\pi r^3}{3}\) = \(\frac{4\pi(4)^3}{3}\) = \(\frac{256\pi}{3}\) x 10-6m3 density(P) = \(\frac{\text{Mass}}{\text{Volume}}\) = \(\frac{64}{\frac{256\pi}{3 \times 10^{-6}}}\) = \(\frac{64 \times 3 \times 10^{-6}}{256}\) = \(\frac{3}{4 \times 10^{-6}}\) m = PV = \(\frac{3}{4 \pi \times 10^{-6}}\) x \(\frac{4}{3}\) \(\pi\)[32 - 22] x 10-6 \(\frac{3}{4 \times 10^{-6}}\) x \(\frac{4}{3}\) x 5 x 10-6 = 5kg
