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in Surface Areas And Volumes by (26.9k points)
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The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is :

A. 2 : 1 

B. 1 : 1 

C. 2 : 3 

D. 1 : 2

1 Answer

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Best answer

Option : (C)

Volume of a sphere = \(\frac{4}{3}\)πr3 

Volume of a cylinder = πr2

If a cylinder circumscrimbes a sphere of radius r, 

then its base radius is ‘r’ and height is diameter = 2r

Ratio between the volume of a sphere and volume of a circumscribing right circular cylinder

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

= 2 : 3

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