be imp

ossible t

o see!

W

ith enough (infini

te)

circles

Area of a circle = ∏r

2

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 sec

t

or

s

ar

e sma

ll enough,

ev

entua

ll

y i

t’s a

p

er

f

ec

t fi

t.

∏

r

2

T

hey ac

tua

ll

y need to be R

EALL

Y

sma

ll, much sma

ller than this, but

if w

e dr

ew them tha

t sma

ll they’d

tr

iangles ther

e ar

e no

rough edges.

you are here 4 231

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

deal. Is MegaSlice really a better value?

If your calcul

a

t

or doesn’t hav

e a

Pi butt

on then y

ou can use 22/7

t

o get an approxima

te v

a

lue f

or Pi.

mario’s is the better value

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

Mar

io’s is MOR

E!

Jus

t pr

ess tha

t “Pi”

button on your ca

lcul

a

t

or.

If your calcul

a

t

or doesn’t hav

e

a Pi butt

on and y

ou used 22/7

ins

tead, y

our number

s will be

slightly dif

f

er

ent but the fina

l

answ

er will be the same.

T

he circle ar

ea

formul

a

Pizza size is

diameter: divide

i

t in ha

lf to

get radius.

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 of tricks that might help you. First of all, if

you can remember that circumference is also found from πD then

you can compare that and find which one matches (2πr). Also, if you

can remember that you learned about circumference before area,

the 2 comes first on the circumference formula, and comes after in

the area formula.

Q:

What if I have to find just the area of a slice of pizza,

and not the whole circle?

A:Sector area is easy to find—just like you used its angle to

find the length of an arc, you can use the sector angle to find sector

area. Find the area of the circle then divide it by 360 (to find the

area of a 1 degree sector) and multiply by the angle of your sector.

232 Chapter 5

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