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Area of a Sector 2665 Views


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Description:

Time to learn about the area of a sector. And no, that's not the sector's bedroom with a bumper sticker on the door that reads, "GO AWAY."

Language:
English Language

Transcript

00:04

Area of a Sector, a la Shmoop.

00:07

The King of Bavaria has a circular plot of land with a radius of 50 meters

00:11

that he’d like to turn into a garden, where he can grow his own Bavarian crème donuts.

00:16

Shh, don’t tell him. It would break his heart.

00:18

He left his gardener the instruction that the garden should be divided into fourteen

00:23

“slices” of equal area, and all of them planted with a different variation of crème donut.

00:30

Before the gardener could ask any questions, the King of Bavaria had skipped away to look

00:33

after his swans. Fortunately, this particular gardener remembered

00:38

his geometry, specifically the formula for the area of a sector, or “slice” of a circle.

00:44

Area equals one-half the radius of the circle times the arc length of the desired sector.

00:51

To find the arc length of the desired sector, we need the radius and central angle in radians:

00:59

An entire circle encompasses 2 pi radians, and the king wants it divided 14 ways,

01:05

so the central angle of each sector would be 2 pi divided by 14.

01:09

2 divided by 14 simplifies to 1 over 7, so we can reduce 2 pi over 14 to pi over 7 radians.

01:17

Multiply this by the radius of the garden, 50 meters, and we have 50 pi over 7 meters

01:23

for the arc length.

01:26

Now we can find the area of the sector.

01:29

1/2 times 50 meters times 50 pi over 7 meters is the same as 25 meters times 50pi over 7 metes.

01:38

This equals 1250 pi over 7 meters squared…

01:42

…roughly 561 meters squared per sector of the garden.

01:47

And now to figure out a way to cultivate donuts.

01:49

The gardener had better come up with something.

01:51

The King gets cranky when he hasn’t gotten his sugar fix.

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