SOLUTION: 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

Algebra ->  Equations -> SOLUTION: 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       Log On


   

Question 947618: 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.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
What volume of ethanol?

11.86%2Agrams%2A%281%2F0.789%29%28mililiter%2Fgram%29=highlight%2815.0317%2Amilliliter%29. You want this to no more than three significant figures: 15.0 mililiters.

Be aware that 1 milliliter is equal to 1 cubic centimeter.
Be aware, diameter is two of the radii.

Your goal asked is find the inner diameter of the cylinder. You have the correct volume formula for a cylinder.

Look at the volume formula, and solve for r.
V=pi%2Ah%2Ar%5E2
pi%2Ah%2Ar%5E2=V
highlight_green%28r%5E2=V%2F%28pi%2Ah%29%29
You want r, not to stop at just r^2.
THIS should make sense: highlight_green%28r=sqrt%28V%2F%28pi%2Ah%29%29%29