Question

Lisa drew three circles to form a figure. The areas of the circles were in the

Answer 1

Answer:

Fraction of the figure shaded = $\frac{13}{16}$

Step-by-step explanation:

Ratio of the areas of the given circles are 1 : 4 : 16

Then the radii of the circles will be in the ratio = $\sqrt{1}:\sqrt{4}:\sqrt{16}$

                                                                             = 1 : 2 : 4

If the radius of the smallest circle = x units

Then the radius of the middle circle = 2x units

and the radius of the largest circle = 4x units

Area of the smallest circle = πx²

Area of the middle circle = π(2x)² = 4πx²

Area of the largest circle = π(4x)²= 16πx²

Area of the region which is not shaded in the middle circle = πx²(4 - 1)

                                                                                                  = 3πx²

Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded

= 16πx² - 3πx²

= 13πx²

Fraction of the figure which is not shaded = $\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}$

= $\frac{13\pi x^{2} }{16\pi x^{2} }$

= $\frac{13}{16}$