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  • Level: GCSE
  • Subject: Maths
  • Word count: 2711

Math Investigative Task - calculating the value of metal used in coins.

Extracts from this document...

Introduction

10B

Maths Investigative Task

By: Aadharsh. D


Part 1

2. The article was written on 11 April 2006.

3.

a) The article mentions that there are 160 pennies in one pound. This means that 160 pennies weigh 0.45359237 kilograms. To find out the weight of one penny in kilograms, divide the weight by the number of pennies. Therefore, it will be 0.45359237 kilograms ÷ 160 pennies = 0.0028349523125 kilograms or 2.8349523125 grams. For ease of calculation, I will be taking it as 2.835 grams.

b) The article mentions that a coin is made up of 97.50% zinc. This means that 97.50% of the total mass of the coin is the mass of the zinc present in the coin. To find out the mass of the zinc, we have to calculate 97.50% of the total mass of one coin. We can calculate this with this calculation: 2.8349523125 x 0.975= 2.7640785046875 grams. For ease of calculation, I will be taking it as 2.764 grams or 0.006 pounds.

c) The article states that a coin is made up of 2.5% copper. This means that 2.5% of the total mass of the coin is the mass of the copper present in the coin. To find out the mass of the copper, we have to calculate 2.5% of the total mass of one coin. We can calculate it with this calculation: 2.8349523125 x 0.025 = 0.0708738078125 grams. For ease of calculation, I will be taking it as 0.071 grams or 0.0015 pounds

4.

...read more.

Middle

Tin: 0.02135 x 0.078 = $0.0016653 or 0.00119845 EUR (0.0012 EUR)

Value of all the metals:

0.0346 + 0.0006 + 0.0005 + 0.00012 = 0.0369 EUR

        The face value of a 50 cent Euro coin is 0.50 EUR. The value of all the metals combined come around to 0.0369 EUR and this is significantly lower than the face value of the coin. Hence, it is not worth melting the Euro coins.

8. The degree of accuracy is pretty high. In some parts I did not round up to make the answer more accurate. For example, in question 7, I did not round up the dollars or the euros because I wanted them to be accurate as possible when I add them up to the total value of the metal. In other questions such calculations, I tried to round up to the third decimal place to make the calculations easier. If I did not round them up, the number becomes too long and it will become harder to use them in calculations. Sometimes I let the number go to the 4th decimal place if the number is too small such as 0.00015 grams. If I rounded that up to 0.0002 grams, it would mess up my calculations and so I left it at the 4th decimal place.

9. In the short term

...read more.

Conclusion

  1. From the article, we know that the 20 cent coin will have double the volume of the 10 cent coin. We have the volume of the 10 cent coin and hence we find the volume of the 20 cent coin by this calculation: 94.2 x 2 = 188.4mm3.

We already have the thickness of the coin which is 1.5mm and we also have the volume and so now we can find the thickness.

V=πr2h

188.4 = 3.14 x 1.5 x r2

188.4 = 4.71 x r2

r2 = 40

r = image06.png

r = 6.32455532mm or 6.3mm

Diameter = radius x 2

Diameter = 6.3 x 2

Diameter = 12.6mm

Hence, the volume of the coin is 188.4mm3, the diameter is 12.6mm and the thickness is 1.5mm.

  1. For 50 cent coin:

Volume of 20 cent coin : Volume of 50 cent coin = 2 : 5

Therefore, Volume of 50 cent coin = 188.4 x = 471mm3

To find the dimensions, we need to calculate at least one dimension using the method I used earlier.

image00.png

image01.png

image02.png

image03.png

image04.png

image05.png

Diameter: V = πr2h

               471 = 3.14 x r2 x 2.1

                  71 = r2

                     r = 8.45 mm

Diameter = 8.45 x 2 = 16.9mm

Hence, the volume of the coin is 471mm3, the diameter is 16.9mm and the thickness is 2.1mm.

       For 1 dollar coin:

Volume of 50 cent coin : Volume of 1 dollar coin = 1 : 2

Therefore, Volume of 1 dollar coin = 471 x 2 = 942mm3

To find the dimensions, we need to calculate at least one dimension using the method I used earlier.

image00.png

image01.png

image02.png

image03.png

image04.png

image05.png

Diameter: V = πr2h

               942 = 3.14 x r2 x 2.6

                  115 = r2

                     r = 10.7 mm

Diameter = 10.7 x 2 = 21.4mm

Hence, the volume of the coin is 942mm3, the diameter is 21.4mm and the thickness is 2.6mm.

4 Different Compositions of Coins

...read more.

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