Archimedes
needed
to
determine
if
a
goldsmith
had
embezzled
gold
during
the
manufacture
of
the
royal
crown
for
King
Hiero
I
of
Syracuse
.
How
would
you
find
out
if
a
crown
was
made
of
gold
or
a
cheaper
alloy
?
How
would
you
know
if
the
crown
was
a
base
metal
with
a
golden
exterior
?
Gold
is
a
very
____________________
metal
(
even
heavier
than
lead
,
though
lead
has
a
higher
atomic
____________________
)
,
so
one
way
to
test
the
crown
would
be
to
determine
its
density
(
mass
per
unit
____________________
)
.
Archimedes
could
use
scales
to
find
the
____________________
of
the
crown
,
but
how
would
he
find
the
volume
?
Melting
the
crown
down
to
cast
it
into
a
cube
or
____________________
would
make
for
an
easy
calculation
and
an
angry
king
.
After
pondering
the
problem
,
it
occurred
to
Archimedes
that
he
could
____________________
volume
based
on
how
much
water
the
____________________
displaced
.
Technically
,
he
didn't
even
need
to
weigh
the
crown
,
if
he
had
access
to
the
royal
treasury
since
he
could
just
compare
the
displacement
of
water
by
the
crown
with
the
displacement
of
water
by
an
____________________
volume
of
the
gold
the
smith
was
given
to
use
.
According
to
the
story
,
once
Archimedes
hit
upon
the
solution
to
his
problem
,
he
burst
outside
,
naked
,
and
ran
through
the
streets
yelling
,
"
____________________
!
____________________
!
"
Some
of
this
might
be
fiction
,
but
Archimedes'
idea
to
calculate
the
____________________
of
an
object
and
its
density
if
you
know
the
object's
weight
was
fact
.
For
a
small
object
,
in
the
lab
,
the
easiest
way
to
do
this
is
to
partly
fill
a
graduated
cylinder
large
enough
to
contain
the
object
with
water
(
or
some
liquid
in
which
the
object
won't
dissolve
)
.
Record
the
volume
of
water
.
Add
the
object
,
being
careful
to
eliminate
air
bubbles
.
Record
the
new
volume
.
The
volume
of
the
object
is
the
initial
volume
in
the
cylinder
subtracted
from
the
final
volume
.
If
you
have
the
object's
mass
,
its
density
is
the
mass
divided
by
its
volume
.
