Explanation:
remember, a whole circle has 360°.
the area of a whole circle is
pi × r²
r being the radius of the circle. and the radius is half of the diameter.
so, in our case, r = 16/2 = 8 cm.
that means the area of the whole circle (360°) would be
pi × 8² = 64pi cm²
but in our case there is a whole sector of the circle missing. the shaded region is the whole circle minus the sector of 45°.
in other words, we need the area of the circular region that is not 360° but simply 360 - 45 = 315°.
the shaded area had the same ratio to the full circle area, as the angle of 315° has to the angle of a full circle (360°) :
315/360 = 7/8.
so, we can actually write
shaded area = 64pi × 315/360 = 64pi × 7/8 =
= 8pi × 7 = 56pi = 175.9291886...cm²