Calculating diameter of a cylinder using 55.34g of mercury metal (d=13.6g/cm3) cylinder is 5.00cm tall?

Question

How do I calculate the diameter of a cylinder with the following info. Mercury metal has a density of 13.6 g/cm3, and 55.34 g of mercury metal fills a cylinder that is 5.00 cm tall?

Answer 1

55.34 g / (13.6 g/cm^3) = 55.34/13.6 cm^3 (volume)

V = ht x area of base = pi r^2 h

r^2 = V / (pi h) = (55.34/13.6) / (5.00 pi)

r^2 = 55.34 / (5*13.6*pi) = 0.2590 cm

r = 0.5090

d = 2r = 1.0179 cm.

Rounding off, the diameter is 1 cm.

Answer 2

We know the volume formula for a cylinder is = (Pi) x radius(squared) x height. So, if you know the mass (55.34g) and the density (13.6g/cm3), you can figure the volume of the mercury. Now just calculate what diameter (r x 2) would equal that volume where height = 5.00cm.

This would be easier with a whiteboard to explain.

Answer 3

Using density, you can discern the volume of Hg. In this case 55.34g /13.6gcm-3 is 4.07 cm3. Since you know your volume, you may solve for the diameter of the cylinder using the volume expression for a cylinder: V=l(3.14)r^2, where l is the length of the cylinder and r is the radius. 2r would be your diameter.

I have qualms with this question, though. Hg is a liquid...

Answer 4

FIRST, DON'T FORGET TO EXPRESS ANSWER TO PROPER NUMBER OF SIGNIFICANT DIGITS, Which would be three. Your answer will round off so that there are 3 numbers in it.

Next,

Convert 55.34 g of mercury to the volume of that mercury in cm3.

55.34g mercury divided by 13.6 g per cm3 gives 4.06912 cm3
(the grams cancel when you divide and you want to keep the extra decimals at this point to keep from losing precision)

Now 4.06912 cm3 is the volume of that cylinder. But you want diameter which is just cm, not cm3 What to do?

Divide 4.06912 cm3 by 5.00 cm to get 0.81382 cm2 (note that one of the cms cancels out to change cm3 to cm2)

This 0.81382 cm2 is the area of the bottom of the cylinder.

Just about everyone will go on about solving for the radius, blah, blah. Why not use an equation that just puts out the diameter?

That equation is sqrt AREA times 1.12838 = DIAMETER

So take the square root of the area, 0.81382 cm2 , giving .90211 cm.
Multiply by 1.12838 [no units] to get 1.01793 cm.

AT THIS POINT ROUND TO 3 SIGNIFICANT DIGITS:

1.02 cm [final answer]
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How to convert the equation for area into equation for diameter, given area.

remember that the diameter is 2 times the radius, so instead of writing AREA = PI times RADIUS squared, lets
write AREA = PI times (DIAMETER / 2) squared.

Rearrange to get diameter by itself:

A=pi(d/2)^2
A/pi=(d/2)^2
A/pi=d^2 / 2^2
A/pi=d^2 / 4
4A/pi=d^2 ; take sqrt of both sides

sqrt(4/pi)(sqrt A)=d
(sqrt AREA) times 1.12838 = diameter

Answer 5

Divide 55,34/13,6/5 You´ll obtain the Area of the base in cm2.

Divide it by Pi and then Square the result, Youll obtain the radius of the base, so multiply it by 2 and youll get the diameter
Aprox. 1,018 cm