A circle with area / blue{9/pi}9πstart color #6495ed, 9, pi, end color #6495ed has a sector with a central angle of / purple{60^/circ}60 ∘ start color #9d38bd, 60, degrees, end color #9d38bd. What is the area of the sector?

Question

Aaden

Mathematics

3 September, 04:24

A circle with area / blue{9/pi}9πstart color #6495ed, 9, pi, end color #6495ed has a sector with a central angle of / purple{60^/circ}60 ∘ start color #9d38bd, 60, degrees, end color #9d38bd. What is the area of the sector?

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Skyla Dunlap · Answer 1

The area of the sector is 3pi/2

Step-by-step explanation:

A sector is that part of a circle bounded by 2 radii and an arc

The circle has an area of 9 pi with a central angle of 60 degrees.

Now the area of the sector is pretty much straight forward to calculate. Since it is a circle, the total angle we have is 360.

Now the sector subtends an angle of 60 degrees at the centre. What this means is that the sector is exactly 1/6 of the circle. meaning that cutting the circle into 6 slices will give the sector.

Thus, the area of the sector is one-sixth the area of the circle.

The area of the sector is thus 1/6 * 9pi = 9pi/6 = 3pi/2 or 3/2 pi