
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.