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Old Nov 14th 2017, 05:36 AM   #1
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Please help! How big does the semi circle need to be?

Hello there,

The problem that one of my students came to me with is:

I want to fit 240 grams of chocolate into a semi circle, so could you tell me the diameter I need to make the semi circle in mm?

I have worked out that the volume of a 100mm diameter semi circle is 5235 cubic mm, but then how do I apply that?

Please help! Many thanks!
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Old Nov 14th 2017, 06:50 AM   #2
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I note that You seem to have had some problems posting...

There is some crucial information missing

What is the volume of 240 grams of chocolate?
litres would be a start,
but then that would need to be converted to cubic mm to fit with the other part of your solution.
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Old Nov 14th 2017, 06:36 PM   #3
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Originally Posted by JJLondon View Post
I have worked out that the volume of a 100mm diameter semi circle is 5235 cubic mm, but then how do I apply that?!
First we need to need to understand the difference between AREA and VOLUME

A 100mm circle has an AREA of 78.5 square centimeters it only has a VOLUME when height is specified ...

You need to tell us how thick the chocolate will be ,

Solid chocolate has a density of 1.056
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Old Nov 15th 2017, 02:25 AM   #4
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How do I go about finding the volume of a material? Such as chocolate, wax or Ink as examples..?

And sorry, i'm talking about a sphere and semi sphere, so the height of the semi sphere is 50mm
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Old Nov 15th 2017, 06:21 AM   #5
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There is a standard equation for calculating the volume of a sphere:
4/3 PI R^3

Where PI =3.13159...
R is the Radius of the Sphere (half the diameter)

you want the volume of a semi-sphere, which is half the above:
2/3 PI R^3

I am assuming the Height of your semi-sphere (5cm) is the radius
(note conversion from millimetres to centimetres, just makes the numbers smaller and easer to deal with).
thus:
2/3 PI * 5^3 = 2.0944 * 125 = 261.8 cubic centimetres
(note that I have rounded some of these numbers off a little).

1 litre is 1000 cubic centimetres
thus the volume of your semi-sphere is 0.2618 litres
(or just over 1/4 litre)

assuming that oz93666 has given the correct value for the density of chocolate and that his units are kilograms per litre then you will need
1.056 *0.2618 = 0.276 kg (276 grams) of chocolate.
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