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: Option A
Explanation
(frac{1sqrt{3}}{(frac{1}{2})^2})
= (frac{4}{sqrt{3}})
= (frac{sqrt{3}}{sqrt{3}})
= (frac{4sqrt{3}}{sqrt{3}})
m = 64kg, V = (frac{4pi r^3}{3})
= (frac{4pi(4)^3}{3})
= (frac{256pi}{3}) x 10-6m3
density(P) = (frac{text{Mass}}{text{Volume}})
= (frac{64}{frac{256pi}{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