An ice cube of edge a is placed in an empty cylindrical vessel of radius 2a. Find the edge (in cm) of ice cube when it just leaves the contact with the bottom assuming that ice melts uniformly maintaining its cubical shape. Take a = 12 `pi` cm (Ice is lighter than water)

Answer

B, C

Explanation

Let xrarr edge of ice block.
when it just leaves contact with the bottom of the glass,
hrarr Height of water method from ice.
here W=U
`rarr (x)^3xxrho_(ice)xxg=(x)^2xxhxxrho_wxxg`
`rarr h=(0.9)x`
Again volume of water formed from melting of ice is given by
`(4)^3-(x)^3=pixx(r)^2xxh-x^I2h`
[because amont of water `=rho(r_2-x_2)hrarr (4)^3-(x)^3=pixx(3)^2xxh-x^2h]`
utting `h=0.9x`
rarr (4)^3-(x)^3pixx(3)^2xx(0.9)x`
solving the above equation we can get
`x=2.26cm`