Quantitative Aptitude Ques 1866

Question: If 64 identical small spheres are made out of a big sphere of diameter 8 cm, what is surface area of each small sphere?

Options:

A) $ \pi cm^{2} $

B) $ 2\pi cm^{2} $

C) $ 4\pi cm^{2} $

D) $ 8\pi cm^{2} $

Show Answer

Answer:

Correct Answer: C

Solution:

  • Volume of small spheres $ =\frac{Volumeofbiggersphere}{Numberofsmallsphere}=\frac{\frac{4}{3}\pi {{(4)}^{3}}}{64} $ $ =\frac{4}{3}\times \frac{\pi \times 4\times 4\times 4}{64}=\frac{4}{3}\pi cm^{2} $ Let radius of small sphere be r'.

$ \therefore $ $ \frac{4}{3}\pi r^{3}=\frac{4}{3}\pi $
$ \Rightarrow $ $ r’=1cm $ Now, surface area of small sphere $ =4\pi r{{’}^{2}}=4\pi cm^{2} $

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