What is the volume? and how to change the unit of the following question? I'm not sure about the (b) part.

This is a gold bar.
a) What is the volume of this gold bar?
b) A jeweler melts down this gold bar in the shape of a sheet where this sheet is 0.000008 mm thin. What is the area of the gold sheet in m² ?
(** be careful that the units are all different)

1 Answer
Mar 12, 2018

A = 40000m^2A=40000m2

Explanation:

First find the volume:
V = AdV=Ad, where dd is depth.
V = ((a+b)/2 * h) * dV=(a+b2h)d
V = ((6+10)/2 * 5) * 8V=(6+1025)8
V = 40 * 8V=408
V = 320cm^3V=320cm3
Convert sheet width to centimetres:
0.000008/10 = 0.0000008 cm0.00000810=0.0000008cm
Divide volume by width:
A = V/wA=Vw
A = 320/0.0000008A=3200.0000008
A = 400000000cm^2A=400000000cm2
In every metre, there are 100 centimetres, therefore, a square with sides xx cmcm is equivalent to a square with sides x/100x100 mm. Applying this logic, we can determine that the same square has an area of x^2x2 cm^2cm2, which is equivalent to (x/100)^2(x100)2 m^2m2, or x^2/10000x210000 m^2m2. We have proved that an area in m^2m2 is equivalent to that same area in cm^2cm2 divided by 1000010000, therefore 400000000400000000 cm^2cm2 == 4000040000 m^2m2.