What is the Area of the Black region?

The black region simply makes half the area of the original circle : $\frac{Area_{circle}}{2} = \frac{\pi R^2}{2} = \frac{100 \pi}{2} = \boxed{50\pi}$ where $R = \frac{diameter}{2} =\frac {20}{2} = 10$

• Radius $= 10$
• Area of entire figure $= \pi (10)^2 = {\color{#3D99F6}{100\pi}}$
• The figure is shaded black and white in equal proportion.
• Black region is half the area $= \dfrac{100 \pi}{2} = \boxed{50 \pi}$

If we switch the small black and white circles, we observe that they are equal in area.

Since black and white are in equal ratio, the black area will be half of the total area.

• Radius = $\frac { Diameter }{ 2 } =\frac { 20 }{ 2 } =10$

Area Of Figure:

• Area = $\pi { r }^{ 2 }={ 10 }^{ 2 }\pi =100\pi$

Area Of Black Region

• Area Of Black Region = $\Large\frac { 100\pi }{ 2 } =\boxed { \quad 50\pi \quad }$