Maths Calculator Ratio Question!!!!

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I know the answers 36:37 but I just don't understand how to get the answer! Could someone please help x Thanks

Question:
There are two watch faces, A and B.
Both watch faces are circular with radius 2cm. The materials used to make both watch faces have the same thickness. A is made entirely of plastic. B has a 20° sector of metal and a 340° sector of plastic. The ratio of the cost per cm2 of the metal to the cost per cm2 of the plastic is 3:2 Work out the ratio of the cost of the materials for A to the cost of the materials for B. Give your answer in its simplest form.
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Zacken
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Zacken
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(Original post by gcsestudyblr)
I know the answers 36:37 but I just don't understand how to get the answer! Could someone please help x Thanks

Question:
There are two watch faces, A and B.
Both watch faces are circular with radius 2cm. The materials used to make both watch faces have the same thickness. A is made entirely of plastic. B has a 20° sector of metal and a 340° sector of plastic. The ratio of the cost per cm2 of the metal to the cost per cm2 of the plastic is 3:2 Work out the ratio of the cost of the materials for A to the cost of the materials for B. Give your answer in its simplest form.
1. Moved to maths.

2. What have you tried? Please show us some working and/or thoughts of your own, thanks!
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Vikingninja
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I would do it as using the values in that ratio in the question per 20 degrees sector. Do ask if what I said is weird because I'm awful at explaining things initially.
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(Original post by Zacken)
1. Moved to maths.

2. What have you tried? Please show us some working and/or thoughts of your own, thanks!
I've really tried but I literally got nowhere. This question came up in my exam and I'm trying to go through the things I didn't understand. I just pretended that face B cost £10. Therefore it would be £6 : £4. Then that's as far as I got. At one point i worked out the area of just the plastic on face B from 340/360 *pi*2^2 which = 11.868 that got me 1 mark out of the 4 marks for the whole question.
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Zacken
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(Original post by gcsestudyblr)
I know the answers 36:37 but I just don't understand how to get the answer! Could someone please help x Thanks

Question:
There are two watch faces, A and B.
Both watch faces are circular with radius 2cm. The materials used to make both watch faces have the same thickness. A is made entirely of plastic. B has a 20° sector of metal and a 340° sector of plastic. The ratio of the cost per cm2 of the metal to the cost per cm2 of the plastic is 3:2 Work out the ratio of the cost of the materials for A to the cost of the materials for B. Give your answer in its simplest form.
Area A is 4\pi only of plastic.

Area B is \frac{340}{360} \times \pi \times 2^2 = \frac{34\pi}{9} of plastic and \frac{2\pi}{9} of metal.
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Vikingninja
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(Original post by Zacken)
Area A is 4\pi only of plastic.

Area B is \frac{340}{360} \times \pi \times 2^2 = \frac{34\pi}{9} of plastic and \frac{2\pi}{9} of metal.
Don't need area to work it out. Just need to apply the cost ratio to the angles.
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Zacken
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(Original post by Vikingninja)
Don't need area to work it out. Just need to apply the cost ratio to the angles.
Well, yeah, you get lucky here because they're both of the same radii and hence their angles are proportional to their area. But can you note that the ratio is specified in cm^2?
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(Original post by Zacken)
Well, yeah, you get lucky here because they're both of the same radii and hence their angles are proportional to their area. But can you note that the ratio is specified in cm^2?
Is it necessary that its noted in workings because its more of a reference to how much they compare to an equal amount?
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username1732491
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(Original post by gcsestudyblr)
I know the answers 36:37 but I just don't understand how to get the answer! Could someone please help x Thanks

Question:
There are two watch faces, A and B.
Both watch faces are circular with radius 2cm. The materials used to make both watch faces have the same thickness. A is made entirely of plastic. B has a 20° sector of metal and a 340° sector of plastic. The ratio of the cost per cm2 of the metal to the cost per cm2 of the plastic is 3:2 Work out the ratio of the cost of the materials for A to the cost of the materials for B. Give your answer in its simplest form.
Imagine splitting each disc up into 360 equal pieces, with each piece spanning 1°. Let's say a piece made of plastic has a cost of 1 unit. By the ratio given, this means a piece the same size made of metal costs 1.5 units.

Think how many units each disc costs. Disc A has 360 plastic pieces, so it costs 360 x 1 = 360 units. Disc B has 340 plastic pieces, and 20 metal pieces, so it costs (340 x 1) + (20 x 1.5) = 340 + 30 = 370 units. Thus the ratio of the cost of A to the cost of B is 360:370 which can be simplified to 36:37.
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(Original post by TimGB)
Imagine splitting each disc up into 360 equal pieces, with each piece spanning 1°. Let's say a piece made of plastic has a cost of 1 unit. By the ratio given, this means a piece the same size made of metal costs 1.5 units.

Think how many units each disc costs. Disc A has 360 plastic pieces, so it costs 360 x 1 = 360 units. Disc B has 340 plastic pieces, and 20 metal pieces, so it costs (340 x 1) + (20 x 1.5) = 340 + 30 = 370 units. Thus the ratio of the cost of A to the cost of B is 360:370 which can be simplified to 36:37.
Thank you! this makes sense!
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