3080 cu cm of water is required to fill a cylindrical vessel completely and 2310 cu cm of water is required to fill it up to 5 cm below the top.Find-
1. radius of the vessel
2. height of the vessel
3. wetted surface area of the vessel when it is half-filled with water

Asked by kriti_bajpai01 | 7th Sep, 2015, 07:22: PM

Expert Answer:

Volume of Cylinder = begin mathsize 14px style Volume space of space cylinder space equals space πr squared straight h The space vessel space is space filled space with space water space completely comma therefore Volume space of space cylinder equals volume space of space water space equals space 3080 space cm cubed space open parentheses given close parentheses therefore πr squared straight h space equals space 3080 space cm cubed space space... open parentheses 1 close parentheses Volume space of space water space when space filled space till space 5 space cm space below space the space top equals space 2310 space space cm cubed space space open parentheses given close parentheses equals space πr squared open parentheses straight h minus 5 close parentheses space equals space 2310 space space cm cubed space space space... open parentheses 2 close parentheses space space Dividing space... open parentheses 1 close parentheses space by space... open parentheses 2 close parentheses comma fraction numerator πr squared straight h over denominator πr squared open parentheses straight h minus 5 close parentheses end fraction equals 3080 over 2310 therefore fraction numerator straight h over denominator straight h minus 5 end fraction equals 308 over 231 rightwards double arrow 231 straight h equals 308 open parentheses straight h minus 5 close parentheses space rightwards double arrow 231 straight h space equals 308 straight h minus 1540 therefore 77 straight h equals 1540 therefore straight h equals 20 space therefore Height space of space the space vesse l equals space 20 space cm Substututing space straight h space equals space 20 space in space... open parentheses 1 close parentheses πr squared straight h space equals space 3080 rightwards double arrow πr squared cross times 20 space equals space 3080 rightwards double arrow πr squared space equals space 154 therefore straight r squared space equals space 154 over straight pi equals 154 space cross times 7 over 22 equals space 49 therefore straight r space equals space 7 space therefore radius space od space vessel equals 7 space cm Surface space area space of space cylinder space equals space 2 πr squared plus 2 πrh But space only space bottom space of space cylinder space gets space wet space and space height space of space wetted space cylinder space when space half space filled space equals space 10 space cm space therefore Surface space area space of space wetted space cylinder space when space half space filled space equals space πr squared plus 2 πrh space space therefore Surface space area space of space wetted space cylinder space when space half space filled space equals open parentheses 22 over 7 cross times 7 squared close parentheses plus 2 cross times 22 over 7 cross times 7 cross times 10 therefore Surface space area space of space wetted space cylinder equals open parentheses 22 cross times 7 close parentheses plus 440 equals 594 space cm squared end style

Answered by Priti Shah | 8th Sep, 2015, 05:36: AM

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