Quantitative Aptitude Ques 1681

Question: Weight of a solid metallic sphere of radius 4 cm is 4 kg. The weight of a hollow sphere made with same metal, whose outer diameter is 16 cm and inner diameter is 12 cm, is

Options:

A) 20.5 kg

B) 15.5 kg

C) 16.5 kg

D) 18.5 kg

Show Answer

Answer:

Correct Answer: D

Solution:

  • Volume of solid sphere of radius $ 4cm=\frac{4}{3}\pi {{(4)}^{3}}cm $ Volume of hollow sphere $ =\frac{4}{3}\pi [{{(8)}^{3}}-{{(6)}^{3}}]cm^{3} $ $ \because $ Weight of $ \frac{4}{3}\pi {{(4)}^{3}}cm^{3}=4kg $

$ \therefore $ Weight of $ \frac{4}{3}\pi [{{(8)}^{3}}-{{(6)}^{3}}]cm^{3} $ $ =\frac{4}{\frac{4}{3}\pi {{(4)}^{3}}}\cdot \frac{4}{3}\pi [{{(8)}^{3}}-{{(6)}^{3}}] $ $ =\frac{4(512-216)}{4^{3}}=18.5kg $