The diagram shows a sector OPQR of a circle, centre O and radius 8 cm - Edexcel - GCSE Maths - Question 8 - 2021 - Paper 3

The area of the sector can be calculated using the formula:

$A_{sector} = \frac{\theta}{360^\circ} \times \pi r^2$

For sector OPQR (with angle 90°), we have:

$A_{sector} = \frac{90}{360} \times \pi \times (8)^2 = \frac{1}{4} \times \pi \times 64 = 16\pi ext{ cm}^2$

Approximating $\pi$ as 3.14, we find:

$A_{sector} \approx 16 \times 3.14 = 50.24 \text{ cm}^2$

The area of the shaded segment PQR can be found by subtracting the area of triangle OPR from the area of the sector OPR:

$A_{shaded} = A_{sector} - A_{OPR}$ $A_{shaded} = 50.24 - 32 = 18.24 \text{ cm}^2$

Rounding this to three significant figures gives: $A_{shaded} \approx 18.2 \text{ cm}^2$