The circumference of circle B is 90% of the circumference of circle A - Edexcel - GCSE Maths - Question 10 - 2019 - Paper 2

To find the ratio of the area of circle A to circle B, we first recognize that the circumference of circle B is 90% of that of circle A.

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

$C_B = 0.9 C_A$

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

Thus: $C_B = 2\pi r_B = 0.9 (2\pi r_A)$

Simplifying gives us: $r_B = 0.9 r_A$

Next, we find the areas of both circles. The area ($A$) of a circle is given by: $A = \pi r^2$

The area of circle A is: $A_A = \pi r_A^2$

The area of circle B is: $A_B = \pi (r_B)^2 = \pi (0.9 r_A)^2 = 0.81 \pi r_A^2$

Now, we express the ratio of the area of circle A to circle B:

$\text{Ratio} = \frac{A_A}{A_B} = \frac{\pi r_A^2}{0.81 \pi r_A^2} = \frac{1}{0.81} = 1.234 : 1$