Hallllllllllllllp

Question

In the diagram, each circle is divided into two equal areas and  is the center of the larger circle. The area of the larger circle is  What is the total area of the shaded regions?

Answer 1

Area of large circle = πr² = 64π. So, the large circle has radius 8.

The diameter of the smaller circle is the same as the radius of the large circle, So, the small circle has

radius 4.

Area of shaded region = (1/2)π(8)² + (1/2)π(4)² = 40π

Answer 2

Hi Abby,

Dimensional analysis might be a neat way to solve this. If a radius is measured in units, area is measured in square units, for example cm². Proportions will follow scale in the same way units do - the smaller circle has half the radius, so it will have (1/2)² = 1/4 the area, of the larger circle.

In the large circle with area 64π, 32π is shaded. The small circle has area (1/4) * 64π = 16π, so 8π is shaded. 32π + 8π = 40π.