Gold, which has a density of `19.32g//cm^(3)`, is the most ductile metal and can be pressed into a thin leaf or drawn out into a longfiber. (a) If a sample of gold with a mass of 29.34 g is pressed into a leaf of `1.000mum` thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius `2.500mum`, what is the length of the fiber?

Explanation

To solve the problem step by step, we will break it down into two parts as given in the question.

### Part (a): Finding the Area of the Leaf

1. **Identify the given values:**
- Mass of gold (m) = 29.34 g
- Density of gold (ρ) = 19.32 g/cm³
- Thickness of the leaf (t) = 1.000 µm = 1.000 x 10⁻⁶ m
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