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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