Question

The area of this circle is 42 π m2. what is the area of a 60° sector of this circle.

this is just to help people :)

Answer 1

The Area of sector is 7
`\pi` m²

Explanation:

Given as , for a circle :

The Area of circle = 42
`\pi` m²

The angle of sector = Ф = 60°

∵ Area of circle =
`\pi` × r² , where r is the radius of circle

or, 42
`\pi` m² =
`\pi` × r²

∴ r² = 42

Now,

Area of sector =
`\pi` × r² ×
`(\Theta )/(360^(\circ))`

Or, Area of sector =
`\pi` × 42 ×
`(\60° )/(360^(\circ))`

or, Area of sector =
`\pi` × 42 ×
`(1)/(6)`

∴ Area of sector =
`\pi` × 7

I.e Area of sector = 7
`\pi` m²

Hence The Area of sector is 7
`\pi` m² . Answer