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# A spherical glass vessel has a cylindrical neck that is 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water the vessel can hold

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This problem depends on vessel structure in the given problem they give information about its dimension. Last time this problem asked in 2009 cbse board exam. Question number 26 from RS Aggarwal book page number 288, exercise 17A chapter volume and surface area of solid.

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1. Given in problem,

Diameter of spherical part = 21 cm

Radius of the spherical part = 10.5 cm

Volume of spherical part of the vessel = [4/3] πr³

= [4/3] × [22/7] × [10. 5]³

= 4851 cm³

∴ Volume of spherical part of the vessel = 4851 cm³

Diameter of cylinder = 4 cm

Radius of cylinder = 2 cm

Height of cylinder = 7 cm

Volume of the cylindrical part of the vessel = πr²h

= [22/7] × 2² ×7

= 88 cm³

∴ Volume of the cylindrical part of the vessel = 88 cm³

Total volume of the vessel = 4851 +88 = 4939 cm³

∴ Total volume of the vessel is 4939 cm³

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