a cylindrical vessel having diameter equal to its height is full of water which is poured into two identicle cylinderical vessel of diameter 42 cm and height 21 cm which are filled completely . find the diameter of cylindrical vessel 
 

Asked by krishan_5 | 7th Feb, 2017, 12:22: PM

Expert Answer:

begin mathsize 14px style Let space the space radius space of space the space cylindrical space vessel space be space straight r.
rightwards double arrow the space diameter space of space the space cylindrical space vessel equals 2 straight r
So comma space the space height space of space the space cylindrical space vessel space is space also space 2 straight r.
Volume space of space the space water space in space each space of space the space identical space cylindrical space vessels
equals πr squared straight h
equals straight pi cross times 21 cross times 21 cross times 21

So comma space volume space of space the space cylindrical space vessel equals 2 cross times open parentheses Volume space of space the space water space in space each space of space the space identical space cylindrical space vessels close parentheses
rightwards double arrow πr squared left parenthesis 2 straight r right parenthesis equals 2 cross times open parentheses straight pi cross times 21 cross times 21 cross times 21 close parentheses
rightwards double arrow straight r cubed equals fraction numerator 21 cross times 21 cross times 21 cross times 2 over denominator 2 end fraction
rightwards double arrow straight r cubed equals 21 cross times 21 cross times 21
rightwards double arrow straight r equals 21 space cm
So comma space the space diameter space of space the space cylindrical space vessel space is space 42 space cm. end style

Answered by Rebecca Fernandes | 7th Feb, 2017, 01:19: PM