Step by step explanation:
To turn degrees into radian yuo have to multiply for the conversion factor, remember that pi radians are equal to 180 degrees, so:
[tex]75^o=75^o\cdot\frac{\pi\text{ rad}}{180^o}=\frac{5\pi}{12}\text{rad}[/tex]
And for the problem we can first find the total area, if 75° is 12cm^2. How much do 360° correspond to?
[tex]\begin{gathered} \frac{A}{360}=\frac{12}{75} \\ A=\frac{12\cdot360}{75} \\ A=57.6cm^2 \end{gathered}[/tex]
Now we can use the area formula:
[tex]A=\pi\cdot r^2[/tex][tex]57.6=\pi\cdot r^2[/tex][tex]\frac{57.6}{\pi}=r^2[/tex][tex]r=\sqrt[]{\frac{57.6}{\pi}}[/tex][tex]r\approx4.3cm[/tex]
The radius is approximately 4.3 cm
