The time needed to empty a vertical cylindrical tank, varies directly as the square root of the height of the tank and the square of the radius. By what factor will the emptying time change if the height is doubled and the radius increased to 25%.

Solution:

We assume emptytime is t, the height of tank is h, the radius is r,

the coefficient is k.

So the formula of t is

t = k*sqrt(h)*r^2

If h'= 2h, r'= 1.25r

t' = k*sqrt(h')*r'^2

   = k*sqrt(2h)*(1.25r)^2

   = sqrt(2)*(1.25)^2*[ k*sqrt(h)*r^2]

   = 2.21t

So t'= 2.21t

So the fator of change of empty time is 2.21