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A cylindrical can of internal diameter 14 m and of height 10 m is used to store water. The cylindrical can is half filled with water and that water is poured into another cylinder which is mounted on hemispherical bowl. The cylinder is 5/6th filled. The radius of cylindrical and spherical part is 3/10th of the radius of can. Find the height of the can.

A cylindrical can of internal diameter 14 m and of height 10 m is used to store water. The cylindrical can is half filled with water and that water is poured into another cylinder which is mounted on hemispherical bowl. The cylinder is 5/6th filled. The radius of cylindrical and spherical part is 3/10th of the radius of can. Find the height of the can. Correct Answer 67.36 m

Given,

Radius of can = 14/2 = 7m

Volume of cylindrical can = πr2h

= 22/7 × 7 × 7 × 10

= 1540 m3

The cylindrical can is half filled only,

Volume of water which is transferred = 1540/2 = 770 m3

Volume of new cylinder = 770 × 6/5 = 924 m3

Radius of cylindrical part = Radius of hemispherical part = 7 × 3/10 = 2.1 m

Given,

⇒ 924 = (22/7 × 2.1 × 2.1 × h) + (2/3 × 22/7 × 2.1 × 2.1 × 2.1)

⇒ 924 = 13.86 h + 19.404

⇒ h = 65.26 m

Total height of Can = 65.26 + 2.1 = 67.36 m

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