Question

What is the area of a 60° sector of a circle with area `42pim^2`?

Answer 1

`7pim^2`

Explanation:

A full circle is `360^@`

Let area of the `60^@` sector = `A_S` and area of the circle = `A_C`
`A_S= 60^@/360^@A_C=1/6A_C`
Given that `A_C=42pim^2`,
`=> A_S=(1/6)*42pim^2=7pim^2`

Answer 2

`7pi` `m^2`

Explanation:

We need to find the area of the sector. For that we use the formula

`color(blue)("Area of a sector"=x/360*pir^2`

Where `x` is the angle on the vertex of the sector(`60^circ`)

(Note: `pir^2` is the area of the whole circle which is `42pi`)

Let's put everything into the formula

`rarrx/360*pir^2`

`rarr60/360*42pi`

`rarr1/6*42pi`

`rarr1/cancel6^1*cancel42^7pi`

`color(green)(rArr7pi` `color(green)(m^2`

Hopefully this helps!!! :)