A cylinder rod formed from silicon is 46.0 cm long and has a mass of 3.00 kg. The density of silicon is 2.33 g/cm^3. What is the diameter of the cylinder? (the volume of cylinder is given by (pi)r^2h, where r is the radius and h is the length)

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A cylinder rod formed from silicon is 46.0 cm long and has a mass of 3.00 kg. The density of silicon is 2.33 g/cm^3. What is the diameter of the cylinder? (the volume of cylinder is given by (pi)r^2h, where r is the radius and h is the length)

Mathematics
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Okay so first we need a couple of equations \[\large Volume_{Cylinder} = \pi r^2 h\] \[\large Density = \frac{Mass}{Volume}\] So...we can first solve for Volume by the fact that we are given the Density and the Mass \[\large Volume = \frac{Mass}{Density} = \frac{3.00kg}{2.33\frac{g}{cm^3}}\] I'll let you finish that...*Note! We need to convert units to make sure we are in 'kg' for both numbers...
so the density would be 2330 kg?
.00233kg?

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There you go 0.00233kg So \(\large Volume = \frac{3.00kg}{0.00233\frac{kg}{cm^3}}=?\)
v=1287.55
Right...so that is our Volume Now we go back to the first equation we have \[\large Volume_{Cylinder} = \pi r^2 h\] We just solved for Volume...we are given \(\large h = 46.0cm\) And we just need to solve for the radius *and then change to diameter* So \[\large r^2 = \frac{Volume}{\pi h}\] \[\large r = \sqrt{\frac{Volume}{\pi h}} = \sqrt{\frac{1287.55cm^3}{46cm\times \pi}} = ?\]
r=2.98
Right...and since we want the diameter...we just multiply the radius by 2 and we're all set!
so 5.97
Correct! But cm of course!
thank you so much
No problem!

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