33. The volume V

cav

of the cavities is the difference between the volume V

cast

of the casting as a whole and

the volume V

iron

contained: V

cav

= V

cast

− V

iron

. The volume of the iron is given by V

iron

= W/gρ

iron

,

where W is the weight of the casting and ρ

iron

is the density of iron. The effective weight in water (of

density ρ

w

) is W

eff

= W

− gρ

w

V

cast

. Thus, V

cast

= (W

− W

eff

)/gρ

w

and

V

cav

=

W

− W

eff

gρ

w

−

W

gρ

iron

=

6000 N

− 4000 N

(9.8 m/s

2

)(1000 kg/m

3

)

−

6000 N

(9.8 m/s

2

)(7.87

× 10

3

kg/m

3

)

=

0.126 m

3

.