tigers4 said:
it says that my answer is incorrect, I multiplied 32.998 by 2 and got 65.996, but its not correct
There's probably some difficulty with rounding and significant figures through the calculations. This can happen when results depend upon small differences between large numbers, and constants with too few significant figures, like taking g = 9.8 (two figures), or pi = 3.14 through the calculations.
In this case it might be best to carry out all the operations symbolically right up to the end. A lot of the constants and calculations will cancel out.
Suppose we let v1 be the volume of iron comprising the shell, v
s be the overall volume of the spherical shell, and v
h be the volume of the hollow. Then
v_s = \frac{4}{3} \pi (r_s)^3
v_h = \frac{4}{3} \pi (r_h)^3
v1 = v_s - v_h
Now, v1 is also determined by the density of iron and the mass of the iron shell as determined by the volume of displaced water.
m_s = v_s \rho_w
v1 = m_s/\rho_{Fe} Volume of iron comprising the shell
v1 = v_s \frac{\rho_w}{\rho_{Fe}}
So now, putting the parts together,
v_s \frac{\rho_w}{\rho_{Fe}} = v_s - v_h
Divide through by v
s to yield
\frac{\rho_w}{\rho_{Fe}} = 1 - v_h/v_s
Note that we still haven't used g, and it looks like the constants in the volume calculations for v
s and v
h are in a position to cancel out. Can you carry on from here to solve for the radius (and then diameter)?
