# Math

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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 its radius. By what factor will the emptying time change if the height is doubled and the radius increased by 25%?

• Math -

t1 = r^2sqrt(h),

t2 = (r+1.25r)^2*sqrt(2h),
t2 = (2.25r)^2*sqrt(2h),
t2 = 5.0625r^2*1.414sqrt(h),
t2 = 7.16r^2*2qrt(h),

t2/t1 = 7.16r^2*sqrt(h) / r^2*2qrt(h) =
7.16.

The emptying time is increased by a factor of 7.16.

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