A mercury drop of radius R splits up into 1000 droplets equal radii. What is the change in surface area?

Explanation

Volume of one drop = Volume of 1000 droplets
`therefore 4/3 piR^3 = 1000 xx 4/3 pir^3`
`therefore R^3 = 1000r^3`
`therefore r = R/10`
Change in surface area = `1000 xx 4pir^2 - 4piR^2`
`4pi [ 1000 xx R^2/100 - R^2]`
dA = `4pi (10R^2 -R^2) = 36 pi R^2`