Will give 10 points! EASY chem question.?

Question

A cylindrical rod formed from silicon is 18.4 long and has a mass of 2.20 . The density of silicon is 2.33 .

What is the diameter of the cylinder? (The volume of a cylinder is given by , where is the radius, and is its length.)

Please explain step by step on how to get the answer. Thanks, and I will give 10 points!

Answer 1

Find the volume of the silicon rod that will be mass / density = 0,94

Now you know that the volume of the cylinder is V = pi * r^2 * h that means that the radius = sqr( V / pi * h ) = sqr (0,94 / 3,14 * 18,4) = 0,128

The diameter will be 0,256.

For you didn't mention the units of measurement you have to check them out.

That's all.

Answer 2

Start with density=mass/volume, rearrange this to solve for volume

so volume=mass/density; you know everything except volume so solve.

Once you have volume use the equation for the volume of a cylinder, which is; volume=[(Pi)(r^2)](h)

rearrange to solve for the radius.

So take the square root of (v)/(pi*h)= r... two times your radius equals diameter.  Hope that helps!!!

Answer 3

First, let's collect our equations:

To find density, you have to know volume and mass.  Density (D) = Mass (m) / Volume (V)

You know density and mass, so we don't need equations for those at the moment.

Volume = L*pi*r^2 (where L is your given length)  We'll keep r (radius) for now, and convert to diameter later, just for simplicity.

If we substitute our volume equation into our density equation, we get:

D = m/(L*pi*r^2)

Multiply both sides by the denominator on the right, and divide both sides by D, and we get:

L*pi*r^2 = m/D

Let's isolate r^2, since we're trying to find r, by dividing both sides by L*pi

r^2 = m/(D*L*pi)

And sqrt both sides:

r = sqrt(m/(D*L*pi)

We know that diameter (little d) is 2r, or r = d/2, so:

d/2 = sqrt(m/(D*L*pi))

And:

d = 2*sqrt(m/(D*L*pi))

Plug in your numbers:

d = 2*sqrt(2.20/(2.33*18.4*pi))

Calculator work yields:

d = 0.256

Of course, it's best to work these problems with the units in them, to verify that your final answer has consistent units with the expected type of answer.  But that should be the answer.

Good luck!