Question

What is the area of the circular sector of a circle of radius 7 cm that subtends a central angle of 35°?

Answer 1

Sector area = `14.97cm^2`

Explanation:

There are 3 parts of a sector which are usually calculated:
the arc length, the sector angle `theta`, and the sector area.

They all represent the same fraction of the circle

Remember: `color(red)("A fraction" = "part"/"whole")`

For example, for a quarter circle:

The sector angle of 90°: `90/360 = 1/4`

The arc length: `"arc length"/"circumference" =1/4`

The sector area: `"sector area"/"area of circle" = 1/4`

So as long as you know what fraction you are dealing with, given the radius, you can calculate any part of the sector.

In this example: `"fraction" = 35/360`

Sector area = `"fraction" xx pi r^2 = 35/360 xx pi 7^2`

=`35/360 xx pi xx 49`

=`14.97cm^2`