Head First 2D Geometry

find your maximum area

282 Chapter 7

The maximum volume allowed is 3 cubic meters. Handily,

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

area our hot tub can have?

The hot tub’s area must be 6m

2

Whichever shape of tub we choose, the area of the hot

tub must be no more than 6 square meters. That way we

know for sure that it’ll only need 3 cubic meters of water

to fill it, and the environmental engineers will be happy.

The shape and size of the tub is completely flexible—

it’s up to us to work out what size and shape of tub

will give us 6 square meters of area and also meet the

band’s requirement: maximum butt-space!

As will we! Saving

water is kind of

important.

Solution

Volume = Area x Depth

3 = Area x 0.5

3 = Area

0.5

6 square meters = Area

Hope you remembered

the units!

The hot tub company

will let us have any

size of any shape.

6m

2

?

6m

2

?

6m

2

?

6m

2

?

6m

2

?

6m

2

?

6m

2

?

6m

2

?

6m

2

?

6m

2

?

And now you’ve got a

2D problem…phew!

Technically, anything less than or equal

to six would be OK with the engineers,

but we want max butt-space, so we

want to push it to the limit.