## anonymous one year ago 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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1. johnweldon1993

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...

2. anonymous

so the density would be 2330 kg?

3. anonymous

.00233kg?

4. johnweldon1993

There you go 0.00233kg So $$\large Volume = \frac{3.00kg}{0.00233\frac{kg}{cm^3}}=?$$

5. anonymous

v=1287.55

6. johnweldon1993

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 $\large r^2 = \frac{Volume}{\pi h}$ $\large r = \sqrt{\frac{Volume}{\pi h}} = \sqrt{\frac{1287.55cm^3}{46cm\times \pi}} = ?$

7. anonymous

r=2.98

8. johnweldon1993

Right...and since we want the diameter...we just multiply the radius by 2 and we're all set!

9. anonymous

so 5.97

10. johnweldon1993

Correct! But cm of course!

11. anonymous

thank you so much

12. johnweldon1993

No problem!