How do you calculate arc length and sector area and why is it calculated like this? You are given sector angle 40 degrees and radius 7cm and asked to give answers to 3sf.

A sector represents a fraction of a circle. The fraction depends on the angle of the sector, X, and the total angle in a circle which is 360, such that the fraction is x/360. In this case the fraction is 40/360 = 1/9. The arc length represents one ninth (1/9) of the circumference. We know that the circumference is given by 2 * pi * radius, therefore the arc length is given by the fraction multiplied by the circumference. Arc length = (1/9) * 2 *pi * 7 = 4.89 cm to 3sf. The sector area represents one ninth (1/9) of the area of a circle. We know the area of the circle is given by pi * r² therefore the sector area is given by the fraction multiplied by the area of the circle. Sector area = (1/9) *pi * 7² = 17.1 cm² to 3sf.