The circumference of circle B is 90% of the circumference of circle A - Edexcel - GCSE Maths - Question 9 - 2019 - Paper 2

To find the ratio of the areas of circle A and circle B, we first denote their circumferences as follows:

Let the circumference of circle A be represented as $C_A$ and the circumference of circle B as $C_B$.

Given that: $C_B = 0.9 C_A$

The radius of a circle can be expressed in terms of its circumference as: $r = \frac{C}{2\pi}$

Thus, we can find the radii of both circles:

• Radius of circle A: $r_A = \frac{C_A}{2\pi}$

• Radius of circle B: $r_B = \frac{C_B}{2\pi} = \frac{0.9 C_A}{2\pi} = 0.9 r_A$

Next, we calculate the areas of both circles:

• Area of circle A: $A_A = \pi r_A^2$
• Area of circle B: $A_B = \pi r_B^2 = \pi (0.9 r_A)^2 = \pi (0.81 r_A^2) = 0.81 A_A$

Now, we can find the ratio of the areas: $\text{Ratio} = \frac{A_A}{A_B} = \frac{A_A}{0.81 A_A} = \frac{1}{0.81} \approx 1.235$

Thus, the ratio of the area of circle A to the area of circle B is approximately (1.235 : 1).