Question

a person have a gold coin of diameter 2cm and thickess 2mm to a goldsmith for melting and drawing into a wire of diameter 1mm . the gold smith gave back a wire of gold of length 76cm with diameter 1mm. if the wastage allowed in melting could be a maximum of 5% of the total volume ,
question is whether gold smith was honest or not

Answer 1

The volume of the coin is given by
\[V _{c}=\frac{\pi d ^{2}}{4}\times x\]
where d is the diameter and x is the thickness.
The volume of the wire is given by
\[V _{w}=\frac{\pi d ^{2}}{4}\times y\]
where d is the diameter and y is the length of the wire.
First you should convert the dimensions to mm in each case.
Diameter of coin =20mm
Length of wire = 760mm
Next calculate the two values of volume and find the percentage reduction in volume of the wire against volume of the coin.

Answer 2

to find percentage in reduction={[V(wire)-V(coin)]*100}V(wire)

Answer 3

no, to find the percentage in reduction , it is given by this formula
=V(wire)-V(coin)/V(coin)*100

Answer 4

k

Answer 5

[(y-x)/x]%

Answer 6

The volume of the coin is the reference amount in the calculation of the percentage reduction in volume. The percentage reduction in the volume of gold originally in the coin is required. Therefore the percentage reduction in volume is
\[\frac{V _{c}-V _{w}}{V _{c}}\times 100\]

Answer 7

for any question if you want to find out the change in percentage then it it given by
=(final value-initial value)/initial value *100

Answer 8

The reduction in volume of gold is
\[\frac{\pi}{4}[(20^{2}\times 2)-760]=?\]

Answer 9

31.4

Answer 10

Using the value of pi in my calculator the reduction in volume = 31.4159 mm^3

Answer 11

yup you r right
@kropot72 , me too getting the same answer

Answer 12

The volume of the coin is
\[V _{c}=\frac{\pi \times 20^{2}}{2}=?\]

Answer 13

200pi

Answer 14

Correct. Percentage reduction in volume of gold originally in coin is
\[\frac{31.4159}{200\times \pi}\times 100=?\]

Answer 15

5.0025

Answer 16

Not quite. The calculation gives the result 4.99999%

Answer 17

k

Answer 18

I get the result 4.99999% on both a Casio and a Sharp calculator.

Answer 19

yup u r right

Answer 20

Cool!

Answer 21

it means gold smith was honest