Head First 2D Geometry

Length

T

hese “s

traight-sided” s

hap

es ar

e

known as prisms—mor

e about those

in Head Fir

st 3D Geometry.

W

idth

you know how to find area

Hot tub volume is area x depth

Calculating the volume of some 3D shapes can get pretty

gnarly, but for the hot tub range it’s simple. The tubs have

straight sides, so the volume can be found from area × depth.

[T

hank

s! Marketing xx]

AREA = length x width

Same depth a

ll ov

er

Q:

This book is called Head First 2D

Geometry, right? So how come we’re

talking about 3D in this chapter?

A:Volume is definitely a 3D topic, and

we cover it in much more detail in Head

First 3D Geometry, but it’s not too bad to

dip your toes in the water is it? Also, we’re

about to turn this problem back into a 2D

one on the next page.

Q:

You’re going to turn a 3D problem

into a 2D problem? How does that

work?

A:The third dimension in the hot tubs

problem is depth. Once we don’t have to

work with the depth anymore it’s just a 2D

problem we’re left with. Hold that thought

to the bottom of the next page.

Q:

What if the tub was deeper at

one end than the other? Or had curved

sides?

A:The area × depth formula only

applies to 3D shapes with straight sides, all

of the same depth, which are perpendicular

to the base. If the hot tub was deeper

at one end we’d need a different way of

working out its volume.

280 Chapter 7

regular polygons

Our complete summer range..

.

A

l

l

St

r

H

o

t T

ubs

T

r

i

-

c

u

z

i

C

h

i

l

l

-

ou

t

-

c

or

n

er

H

ex

-

i

t

-

u

p

7

t

h

H

eav

en R

el

ax

i

v

8

9

s

i

d

es

M

ag

i

c

C

i

r

c

l

e

T

ubs can be an

y size,

all depths 0.5m

Ok—so all the hot tubs

have the same depth. Does

that help simplify the

problem?

Yes. All the depths are the same, so only

the area of the hot tubs varies.

The All Star Hot Tubs range is a fixed depth: 0.5 meters.

You can have your tub wider and longer, but you can’t

have it deeper.

W

e know wha

t the depth

of any hot tub is.

The maximum volume allowed is 3 cubic meters, and all

the tubs are 0.5 meters deep. What’s the maximum area

our hot tub can have?

you are here 4 281