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How many spheres 6 cm in radius can be made from a metallic 8 cylinders of radius 4 cm and height 90 cm?

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answer is A.

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Detailed Solution

Given, 8 cylinders of radius 4 cm and height 90 cm.
Total volume of the cylinders = number of cylinder

\times

volume of each cylinder

= 8 \times π r^{2} h

= 8 (π (4^{2}) (90))

= 36205.714 c m^{3}

Volume of each sphere is

\frac{4}{3} π r^{3}

= \frac{4}{3} π (6^{3})

= 905.143 c m^{3}

Number of spheres = Total volume of cylinders

\div

volume of each sphere
=

\frac{36205.714}{905.143}

= 40

So, the number of spheres is 40.
Hence, option 3 is correct.

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