The diameter of a circle is 1. What is the area of the circle?

The diameter of a circle is 1. What is the area of the circle ?

$$\small{\text{Diameter $\,d = 1 $}}$$   

$$\small{\text{Radius $\,r= \frac{d}{2} = \frac{1}{2} $}}$$

$$\small{\text{Area $\,A=\pi\cdot r^2 $}}\\
\small{\text{$A=\pi\cdot \frac{1}{2}\cdot \frac{1}{2}$}}\\
\small{\text{$A=\frac{\pi}{4}$}}\\
\small{\text{$A=\frac{3.14159265359}{4}$}}\\
\small{\text{$A=0.78539816340$}}
$}}$$

The formula for the area of a circle is $${\mathtt{A}} = {\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{r}}}^{{\mathtt{2}}}$$ (r = radius)

The diameter of a circle is twice the radius. 

So $${\mathtt{A}} = {\mathtt{\pi}}{\mathtt{\,\times\,}}{\left({\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{D}}\right)}^{{\mathtt{2}}}$$

$${\mathtt{A}} = {\mathtt{\pi}}{\mathtt{\,\times\,}}{\left({\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{1}}\right)}^{{\mathtt{2}}}$$

$${\mathtt{A}} = {\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{0.5}}}^{{\mathtt{2}}}$$

$${\mathtt{A}} = {\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{0.25}}$$

$${\mathtt{A}} = {\mathtt{0.785}}$$ square units (3 d.c.p.)

Did you get some of my cake Zac and Heureka.  There is plenty to go around :)

Yeah but I couldn't finish my whole slice. It seems a waste to waste infinate cake. Anyone else want it?

Yea, why not, I'll have it.  Like you said, we don't want to waste it.   

Imagine how fat you would be if your mum told you, you had to eat it all!  I suppose it woud delay your homework for all eternity   :D

Not the worst way to spend eternity. 

Heureka here is your peice.  You can come back for lots more if you want.

There are an infinite number of slices :)