Question about V=pi r^2 h formulat to solve diameter

timer Asked: Feb 14th, 2015

Question Description

I don’t know how to handle this Algebra question and need guidance.

this has to do with finding the diameter of a 15.0 cm long cylindrical glass tube, sealed at one end with ethanol. The mass of ethanol needed to fill the tube is found to be 11.86 g. the density of ethanol is 0.789 g/mL. calculate the inner diameter of the tube in meters.

my question is : why when we use V=(Pi)r^2(h)  - we find volume is 15.03cm3, height is 15.0 cm, now when I find this answer online they solve diameter by taking r= (the square root of) V / (pi)(h), but in my book they solve differently.
they put the side of the equation with V/(pi)(h) in brackets and take the half root of that.
so it looks like this in the book: r=[V/(pi)(h)]1/2  ----- 1/2 being to the 1/2 power.
so are these two methods the same? is the square root the same as to the 1/2 power? or are these two methods incompatible?
thank you.

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