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Circles Videos 25 videos
This video can run circles around other videos about circles. Sir Cumference, of Round Table fame, explains all the properties of… well, circles....
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."
Equations of circles are a no-brainer. If aliens can do it, so can you. All you do is substitute the center of the circle's coordinates into the eq...
Area of a Sector 2667 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."
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
Full Transcript
- 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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