Question

this square contains several circles. determine the radius and diameter of circles a and b.

Explanation:

Step1: Recall the relationship between radius and diameter

The diameter \(d\) of a circle is related to the radius \(r\) by the formula \(d = 2r\), or \(r=\frac{d}{2}\).

Step2: Analyze circle \(a\)

The side - length of the square is \(4\) cm. The diameter of circle \(a\) is half of the side - length of the square. So \(d_a=\frac{4}{2}=2\) cm. Then, using the formula \(r = \frac{d}{2}\), \(r_a=\frac{d_a}{2}=\frac{2}{2} = 1\) cm.

Step3: Analyze circle \(b\)

The diameter of circle \(b\) is equal to the side - length of the square. So \(d_b = 4\) cm. Then, using the formula \(r=\frac{d}{2}\), \(r_b=\frac{d_b}{2}=\frac{4}{2}=2\) cm.

Answer:

Circle	Radius (cm)	Diameter (cm)
\(b\)	\(2\)	\(4\)