SATHEE: Quantitative Aptitude Ques 521

Quantitative Aptitude Ques 521

Question: A cylinder whose height is $ \frac{2}{3} $ of its diameter has same volume as that of a sphere of radius 8 cm. The radius of base of the cylinder is

Options:

A) 8 cm

B) 4 cm

C) 2 cm

D) 5 cm

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Height of the cylinder $ =\frac{2}{3}\times $ [Diameter of sphere Height $ =\frac{4\times Radius}{3} $ [ $ \because $ Diameter $ =2\times $ Radius] Volume of sphere $ =\frac{4}{3}\pi \times {{(8)}^{3}} $ Now, volume of cylinder $ =\pi r^{2}\times h=\pi \times r^{2}\times \frac{4r}{3} $

$ \Rightarrow $ $ \frac{4}{3}\times \pi \times {{(8)}^{3}}=\pi \times r^{2}\times \frac{4r}{3} $

$ \Rightarrow $ $ 4\times 512=4r^{3} $
$ \Rightarrow $ $ r=8,cm $ Alternate Method Height of the cylinder $ =\frac{4}{3}\times Radius $ Hence, radius of the sphere and cylinder are same i.e. 8 cm.

Quantitative Aptitude Ques 520

Quantitative Aptitude Ques 522

Quantitative Aptitude Ques 521

Question: A cylinder whose height is $ \frac{2}{3} $ of its diameter has same volume as that of a sphere of radius 8 cm. The radius of base of the cylinder is

Options:

Answer:

Solution:

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