Question

What is the major sector? (formula as well?)

Answer 1

Area of major sector is `274.89` units.

Explanation:

If `r` is the radius of a circle, then

area of circle is `pir^2`.

When we draw the sector `BAC`, where `m/_BAC=45^@`,

circle is divided in two parts - one is smaller sector `BAC` formed by arc `BC`, other is larger i.e. major sector `BDCA`. The angle formed by latter is `360^@-45^@=315^@`.

As `360^@` comprises of area `pir^2`, a sector with an angle `theta` in degrees has an area of `(pir^2theta)/360`. In the given case `r=AC=10` and as we want

and area of major sector is `(pixx10^2xx315)/360`

Let us assume `pi=3.1416`, hence area of major sector is

`(3.1416xx100xx315)/360=(314.16xx7)/8=274.89`