The circumference of circle B is 90% of the circumference of circle A - Edexcel - GCSE Maths - Question 11 - 2019 - Paper 2

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

According to the problem, we have: $C_B = 0.9 C_A$

The circumference of a circle is related to its radius $r$ by the formula: $C = 2 \pi r$

Thus, we can express the circumferences in terms of their respective radii: $C_A = 2 \pi r_A$ and $C_B = 2 \pi r_B$

Substituting these into the equation gives: $2 \pi r_B = 0.9 \cdot (2 \pi r_A)$ This simplifies to: $r_B = 0.9 r_A$

Now, we can find the areas of the circles: $A_A = \pi r_A^2$ and $A_B = \pi r_B^2$

Substitute $r_B = 0.9 r_A$ into the area of circle B: $A_B = \pi (0.9 r_A)^2 = \pi (0.81 r_A^2)$

Therefore, the ratio of the areas is: $\frac{A_A}{A_B} = \frac{\pi r_A^2}{\pi (0.81 r_A^2)} = \frac{1}{0.81}$

Thus, the ratio of the area of circle A to the area of circle B is approximately: $\frac{100}{81}$.