Question

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)

Answer 1

`A = 40000m^2`

Explanation:

First find the volume:
`V = Ad`, where `d` is depth.
`V = ((a+b)/2 * h) * d`
`V = ((6+10)/2 * 5) * 8`
`V = 40 * 8`
`V = 320cm^3`
Convert sheet width to centimetres:
`0.000008/10 = 0.0000008 cm`
Divide volume by width:
`A = V/w`
`A = 320/0.0000008`
`A = 400000000cm^2`
In every metre, there are 100 centimetres, therefore, a square with sides `x` `cm` is equivalent to a square with sides `x/100` `m`. Applying this logic, we can determine that the same square has an area of `x^2` `cm^2`, which is equivalent to `(x/100)^2` `m^2`, or `x^2/10000` `m^2`. We have proved that an area in `m^2` is equivalent to that same area in `cm^2` divided by `10000`, therefore `400000000` `cm^2` `=` `40000` `m^2`.