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 is A

\(\frac{1\sqrt{3}}{(\frac{1}{2})^2}\)

= \(\frac{4}{\sqrt{3}}\)

= \(\frac{\sqrt{3}}{\sqrt{3}}\)

= \(\frac{4\sqrt{3}}{\sqrt{3}}\)

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