Head First 2D Geometry

you are here 4 231

circles

Area of a circle = ∏r

2

Use the circle area formula to work out the area of the pizza in each

deal. Is MegaSlice really a better value?

It’s true—if you crammed enough narrow triangles into a circle,

eventually you’d get a perfect fit. You’d need an infinite number of

triangles, but it turns out the number of triangles cancels neatly, so

wham—you just found the formula for the area of a circle!

If your sectors

are small enough,

eventually it’s a

perfect fit.

∏

r

2

They actually need to be REALLY

small, much smaller than this, but

if we drew them that small they’d

be impossible to see!

If your calculator doesn’t have a

Pi button then you can use 22/7

to get an approximate value for Pi.

With enough (infinite)

triangles there are no

rough edges.

mario’s is the better value

232 Chapter 5

Use the circle area formula to work out the area of the pizza in each

deal. Is MegaSlice really a better value?

Area = ∏r

2

Mario’s 18” pizza: radius = 18 = 9 inches

2

Area =

∏ x 9

2

= ∏ x 81 = 254.5 sq inches

MegaSlice 12” pizza: radius = 12 = 6 inches

2

Area = 2 x

∏ x 6

2

= 2 x ∏ x 36 = 226.2 sq inches

18”

12” 12”

2 pizzas

Mario’s is MORE!

Q:

Eek—2πr and πr

2

look pretty similar don’t you think? Is

there a way to keep them straight so I don’t mix them up?

A: There are a couple ...