Question

If the diameter of circle a measures half of the diameter of circle b, then the area of circle b is how many times the area of circle a ?

Answer 1

Circle b:

Diameter = x

Radius = $\frac{x}{2}$

Area = $\pi r^{2} = \pi ( \frac{x}{2} )^{2} = \frac{ \pi x^{2} }{4}$

Circle a:

Diameter = $\frac{x}{2}$

Radius = $\frac{x}{2} * \frac{1}{2} = \frac{x}{4}$

Area = $\pi r^{2} = \pi ( \frac{x}{4} )^{2} = \frac{ \pi x^{2} }{16}$

Thus,

Area of circle b to area of circle a

= $\frac{ \pi x^{2} }{4}$ ÷ $\frac{ \pi x^{2} }{16}$

= $\frac{ \pi x^{2} }{4}$ × $\frac{ 16 }{\pi x^{2}}$

= 4

Hence, the area of circle b is 4 times the area of circle a.