Question

If the area of a sector of a circle is 54π and the radius of the circle is 8, then what is the measure of the central angle of the sector?
Show ALL of your work.

Answer 1

Answer:

You can use this app to solve this problem Snapsolve

Step-by-step explanation:

I hope it is useful for you ☺️

Answer 2

Answer:

$\huge{\boxed{\rm{\red{answer=303.75°}}}}$

Step-by-step explanation:

Given:-

the area of a sector of a circle is 54π

and the radius of the circle is 8

To find:-

what is the measure of the central angle of the sector?

Solution:-

Radius of the circle(r)=8 units

Area of the sector(A)=54π sq.units

Let the central angle of the sector be X°

We know that

Area of the sector(A)=(X°/360°)×πr²

=>X°×π×8²/360°=54π

Cancelling π

=>X°×64/360°=54

=>X°8/45°=54

=>X=54×45/8

=>X=27×45/4

>X=1215/4

=>X=303.75°

Answer:-

The central angle of the sector =303.75°