Math CentralQuandaries & Queries


Question from fae, a student:

what is the area of the remaining portion of a large circle with radius 12cm and the seven smaller and equal circles just fit inside?

Hi Fae,

Is this the diagram you have in mind?


I let R be the radius of the larger circle so R = 12 cm. Let r be the radius of the smaller circles. What is the relationship between R and r? What is the value of r?

Find the area of the large circle. Find the area of each of the smaller circles. By subtraction find the area of the part of the larger circle that remains if you remove the 7 smaller circles.


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