The shape ABCDOA, as shown in Figure 1, consists of a sector COD of a circle centre O joined to a sector AOB of a different circle, also centre O - Edexcel - A-Level Maths Pure - Question 4 - 2017 - Paper 1

To determine the area of the shaded sector AOB, we first need to know the angle AOB. Since AOD is a straight line of length 12 cm, we can find the angle using:

$AOB = \pi - \theta = \pi - 0.4 \approx 2.74$ radians.

The area of a sector can be calculated with the formula:

$\text{Area} = \frac{1}{2} r^2 \theta$

Given that the radius $r$ (i.e., $OD$) is 7.5 cm and $\theta$ is 0.4 radians:

$\text{Area} = \frac{1}{2} \times (7.5)^2 \times 0.4$

Calculating this gives:

$\text{Area} = \frac{1}{2} \times 56.25 \times 0.4 = 11.25 ext{ cm}^2$.

Finally, the area of the shaded sector AOB can be found using the total area of sector AOD minus the area of sector COD:

$\text{Area AOB} = \text{Area AOD} - \text{Area COD}$

Since we already have the areas calculated, we can now determine:

Therefore:

• Approximate area of AOB is $27.8\text{ cm}^2$.