$\delta_{co} = \delta_{st} = \delta$
$\left( \dfrac{PL}{AE} \right)_{co} = \left( \dfrac{PL}{AE} \right)_{st}$
$\left( \dfrac{\sigma L}{E} \right)_{co} = \left( \dfrac{\sigma L}{E} \right)_{st}$
$\dfrac{\sigma_{co} L}{14000} = \dfrac{\sigma_{st} L}{200\,000}$
$100 \sigma_{co} = 7 \sigma_{st}$
When σst = 120 MPa
$100 \sigma_{co} = 7(120)$
$\sigma_{co} = 8.4 \, \text{ MPa} \gt 6 \, \text{ MPa}$ → (not okay!)
When σco = 6 MPa
$100(6) = 7 \sigma_{st}$
$\sigma_{st} = 85.71 \, \text{ MPa} \lt 120 \, \text{ MPa}$ → (okay!)
Use σco = 6 MPa and σst = 85.71 MPa.
$\Sigma F_V = 0$
$P_{st} + P_{co} = 300$
$\sigma_{st} \, A_{st} + \sigma_{co} \, A_{co} = 300$
$85.71A_{st} + 6 \, [ \, \frac{1}{4} \pi(200)^2 - A_{st} \, ] = 300(1000)$
$79.71A_{st} + 60\,000 \pi = 300\,000$
$A_{st} = 1398.9 \, \text{ mm}^2$ answer