Question

What's the area of a sector of a circle that has a diameter of 10 in. if the length of the arc is 10 in.?

A. 100 sq in.
B. 75 sq in.
C. 25 sq in.
D. 50 sq in.

Answer 1

Diameter = 10 inches
Radius = Diameter/2 = 10/2 = 5 inches.

Length of arc =
`(Angle \: subtended \: by \: it)/(360) * 2πr`

Now,
Putting values,


`10 = (Angle \: subtended \: by \: it)/(360) * 2 * (22)/(7) * 5 \\ Angle \: subtended \: by \: it = (10 * 360)/(2 * (22)/(7) * 5) \\ Angle \: subtended \: by \: it = (360 * 7)/(22)`

Area of sector =


`(Angle \: subtended \: by \: it \: at \: centre)/(360) * π {r}^(2) \\ ( (360 * 7)/(22) )/(360) * (22)/(7) * {5}^(2) \\ (7)/(22) * (22)/(7) * 25 \\ 25 \: {inches}^(2)`

Area of sector will be C. 25 inches².