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# if the hight of a cylinder is 4 inches, and the volume is 15 ml, whats the diameter?

if the hight of a cylinder is 4 inches, and the volume is 15 ml, whats the diameter?

### 2 Answers by Expert Tutors

Francisco E. | Francisco; Civil Engineering, Math., Science, Spanish, Computers.Francisco; Civil Engineering, Math., Sci...
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V=(∏D2/4)*h
Plugging all the data in the above formula, we obtain:
15=(∏D2/4)*4*2.54
D2= 1.90 cm
D= 1.38 cm
D= 0.54 inches
For 10 ml D2will be 1.2666
D will be 1.1254 cm and
D= 0.443 inches
for the 20Ml D2 = 2.532

I made a big mistake because I though that the volume was given in inches3, I already fixed it, thanks to the tutor.

what would be the answer if the ml was 10, and 20??
Stephen K. | Physics PhD experienced in teaching undergraduatesPhysics PhD experienced in teaching unde...
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Zack,

1st of all we need to get everything into a consist system of units.  For the volume V = 15 mL,
one mL = 1 cm , so rather than try to convert this to cubic inches lets work with cm since the conversion from inches to cm is straight forward.  1 inch = 2.54 cm, so 4 inches x 2.54 cm per inch = 10.16 cm.

Now for a cylinder, volume = height (h) x area of the base (pi*radius squared).

so V = h*pi*r²

To find r we rearrange:  r² = V/(h*pi) , so r = [V/(h*pi)]½

and d = 2*r

Solving for r we get r = [15 cm 3 /(10.16 cm * 3.14)] ½ = 0.69 cm

then d = 2*r =1.4 cm

Let's check our result.  V = h*pi*r² , so V = 10.16 cm * pi * (0.69 cm)² = 15.2 cm³ ,

so we're right back where we started within round off errors.

Now if you like you can convert d = 1.4 cm back to inches :  1.4 cm / 2.54 cm per inch = 0.55 inches