Question

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)

Answer 1

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...

Answer 2

so the density would be 2330 kg?

Answer 3

.00233kg?

Answer 4

There you go 0.00233kg

So \(\large Volume = \frac{3.00kg}{0.00233\frac{kg}{cm^3}}=?\)

Answer 5

v=1287.55

Answer 6

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

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

Answer 7

r=2.98

Answer 8

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

Answer 9

so 5.97

Answer 10

Correct! But cm of course!

Answer 11

thank you so much

Answer 12

No problem!