The magnetic flux ${\mathrm{\varnothing }}_B$ through the surface or loop of vector area $A$ is the magnetic field or number of field lines passing through the surface. It is defined as:
${\mathrm{\varnothing }}_H=B\cdot A,=BA\cos \theta$
Where:
$B=$ magnitude of the magnetic field,
$A=$ area of the surface/loop $\left(m^2\right)$
$\theta =$ angle between the magnetic field lines and the normal or perpendicular to the surface.
where $n=$ normal to the surface loop with area $A$.
Key note:
The key idea to the problem at hand is to note that since the loop is placed in the $x-y$ plane, the normal $n$ to the surface will be in the $z$ - direction. Also, it is stated in the problem that the magnetic field is pointing in the positive $z$ - direction, thus, the normal $n$ to the surface and the magnetic field are in the same direction. So $\theta =0$. See the figure belowinally, using
$$\begin{array}{rl}{\mathrm{\Phi }}_B& =Ba\cos \theta \\ & =\pi r^2\\ {\mathrm{\Phi }}_B& =0.36\times \frac{22}{7}\times {0.25}^2\\ {\mathrm{\Phi }}_B& =\frac{0.495}{7}=0.07wb\end{array}$$