Explanation:
your teacher was very nice and warned you about the trap in the question.
so, really, what do we have to do ?
a full circle represents 360°.
the shaded sector is the full circle minus the white sector !
this is the same as directly calculating the shaded sector for 360-75 = 285°.
so, the area of a circle is
pi×r²
in our case
pi×20² = 400pi
the needed fraction of the whole circle is either
75/360, if we want to subtract it for the solution
or
285/360, if we want to calculate the solution directly.
both lead to the same result.
400pi×360/360 - 400pi×75/360 =
= 400pi × 285/360 = 10pi × 285/9 = 2850pi/9 =
= 316.6666666...pi ≈ 316.7pi