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Volume Videos 8 videos
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Volumes of Pyramids and Cones old 1691 Views
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Description:
The formulas for the volumes of pyramids and cones are strangely similar. Actually, they're exactly the same: just multiply 1/3 by the base area by the height. Easy to remember, right? You'll be ready for the day when Egypt decides to fill up one of the Great Pyramids with water and turn it into a public swimming pool. They'll definitely want to know how to find the volume of a pyramid.
Transcript
- 00:04
Volumes of Pyramids and Cones, a la Shmoop. Pharaoh Tut is on his way to the hereafter,
- 00:11
and he may have overdone it with his list of things to bring to the underworld.
- 00:17
Help him calculate the volume of his pyramid so he'll know if he's going to have to leave
- 00:21
some stuff behind. The length and width of the base are 10 meters
- 00:25
and the height of Tut's pyramid is 12 meters.
Full Transcript
- 00:29
The volume of a pyramid is one-third the volume of the prism with the same base.
- 00:36
Because we have a square base, we know that its area is length times width, which is just
- 00:41
100 meters squared.
- 00:44
We plug that into our formula and solve for the volume. One-third times 100 times the
- 00:50
height of 12. 100 times 12 equals 1200, divided by 3 equals 400.
- 00:57
His neighbor, Pharaoh Irving, is going to meet his maker in a cone rather a pyramid,
- 01:04
so he'll have to use the formula one-third...pi times radius squared times height to find
- 01:10
the volume of the cone.
- 01:12
If we look closely at the volume formula of a cone, it looks a lot like the volume formula
- 01:17
of a pyramid...
- 01:18
...since pi times radius squared is the area of a circle, which is the shape of a cone's
- 01:24
base...and B is the area of the base of a pyramid.
- 01:28
If the radius of the cone's base is 10 and the height is 12, we can plug them into our
- 01:33
formula...
- 01:34
1/3 times pi times 10 squared times height....equals 1/3 times pi times 100 times 12. 1200 divided
- 01:48
by 3 equals 400...so our answer is....400 pi.
- 01:54
Since 400 pi is bigger than 400...looks like Pharaoh Irving is really going to be the one
- 02:00
living
- 02:11
the good... afterlife.
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