Question

The length of an arc of a circle is 7.5 cm. The corresponding sector area is 37.5 cm². The radius is 5cm.

Find the angle subtended at the centre of the circle by the arc.

Answer 1

Answer: Let us assume that the radius of the circle is r where the corresponding sector area and arc length are 37.5sq. cm and 7.5cm. From the given arc length of 7.5cm, the subtended angle at the circle center theta radian can be Theta /2π =7.5/2πr or

Theta radian =7.5/r. For the radian, 7.5/r subtended angle sector area can be 7.5/r/2π^2 or 7.5/2πr*πr^2 or 7.5r/2. We already have given sector area as 37.5, then 7.5r/2=37.5, or r will be 37.5*2/7.5 which gives us 10.

Explanation:

Let us assume that the radius of the circle is r where the corresponding sector area and arc length are 37.5sq. cm and 7.5cm

By the arc length of 7.5cm, the subtended angle at the circle center theta radian will be

Theta /2π =7.5/2πr or

Theta radian =7.5/r

For the 7.5/r radian subtended angle sector area is

7.5/r/2π^2 or 7.5/2πr*πr^2 or 7.5r/2

We have given the sector area 37.5, so now 7.7r/2=37.5, or

r=37.5*2/7.5=10cm