Question

Question 7 - Perimeter and Area of Sectors

sector of a circle
11cm=radius
16cm=arc length
work out the angle in the centre

Answer 1

83.3°

Explanation:

To calculate the size of the central angle of a sector of a circle, given the radius and arc length, we can use the following formula:

`\large\boxed{\theta = (180^(\circ)s)/(\pi r)}`

where:

• θ is the central angle (in degrees).
• s is the arc length.
• r is the radius.

In this case:

• s = 16 cm
• r = 11 cm

Substitute these values into the formula and solve for θ:

`\theta = (180^(\circ)\cdot 16)/(\pi \cdot 11)`

`\theta = (2880^(\circ))/(11\pi)`

`\theta = 83.33931565...^(\circ)`

`\theta = 83.3^(\circ)\; \sf (1\;d.p.)`

Therefore, the size of the central angle is 83.3° (rounded to one decimal place).