Expert: Josh - 8/22/2006

Question
i just join the food processing business...
i have a machine which produce burger with a cylinder mold plate of 92mm in diameter.
this machine will produce burger (92mm in diameter and 9.5mm in thickness)...
this burger weight is 80gram.

i have problem in coverting the volume (which is now in milimetersquare) into gram...

And the other thing is i need to produce a burger with 70gram in weight not 80gram.
the only variable that i can change is the diameter of the burger. the thickness is constantly 9.5mm...

hope u can help me... thanx

Answer
You've worked up quite an appetite in me. Burgers huh?

What we need is the density which is defined precisely as weight over volume.

A circular piece with diameter d=9.2cm and thickness t=0.95cm has volume V, given by V=(pi*r^2)*t, where radius r=d/2, pi is approximately 22/7.

So, the volume here is approximately V = (22/7)*4.6*4.6*0.95 = 63.1523 cm^3 (cubic centimeter).

Dividing the weight, 80 g (grams) by V gives 1.2668 g/cm^3 (gram per cubic centimeter).

If you downsize the burger to 70 g, the size (i.e., volume) of the burger should be reduced to 70/1.2668=55.2583 cm^3 (cubic centimeter).

Keeping the thickness of each slice constant (t=0.95 cm), we solve pi*(r^2)*t = V' for r; where new volume V'=55.2583.

To achieve a weight of 70 g, the radius of the burger needs to be r=square_root_of(V'/(pi*t))=sqrt(55.2583/(3.1415*0.95)), this equals 4.30 cm.

ANSWER: The diameter needs to be adjusted to 8.6 cm.

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Recapping, given weight W, density Q=W/V, where volume V=pi*(r^2)*t. The value of "pi" is approximately 22/7 (or 3.1415), r is the radius, t is the thickness.

Here, density was determined to be Q=1.2668 g/cm^3 (gram per cubic centimeter).

So, for a target weight W, V=W/Q.
The diameter is then given by d = 2r = 2*sqrt{(W/Q)/(pi*t)}.
The parameters W, Q, pi and t are all known.