The diagram below shows a sector of a circle - AQA - A-Level Maths Pure - Question 3 - 2019 - Paper 1

To calculate the area of a sector of a circle, we can use the formula:

$A = \frac{1}{2} r^2 \theta$

where:

• ( A ) is the area of the sector,
• ( r ) is the radius of the circle,
• ( \theta ) is the angle in radians.

Plugging in the known values:

• Radius ( r = 4 ) cm
• Angle ( \theta = 0.8 ) radians

We get:

$A = \frac{1}{2} (4)^2 (0.8)$

Calculating this:

$A = \frac{1}{2} \times 16 \times 0.8 = \frac{16 \times 0.8}{2} = 12.8 \div 2 = 6.4 \text{ cm}^2$

Thus, the area of the sector is ( 6.4 \text{ cm}^2 ).