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

**Question description**

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.

## Tutor Answer

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors