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Volume Videos 8 videos
Volume is crucial to our lives. It determines the amount of food we eat, the amount of fluid we drink, and hydraulics, just to to name a few. One o...
ACT Math: Plane Geometry Drill 3, Problem 2. Can you find the volume of this right circular cylinder?
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...
Volumes of Pyramids and Cones (New) 1852 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.
- 00:08
Pharaoh Tut is on his way to the hereafter, and he may have overdone it with his list [image of Pharaoh Tut]
- 00:12
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 [Image of Egyptians with Pyramid and other monuments]
- 00:21
some stuff behind.
Full Transcript
- 00:23
The length and width of the base are 10 meters and the height of Tut's pyramid is 12 meters. [Explanation for calculating the volume of a pyramid]
- 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 [Explanation for calculating the volume of a pyramid]
- 00:41
100 meters squared.
- 00:44
We plug that into our formula and solve for the volume. [Explanation for calculating the volume of a pyramid]
- 00:48
One-third times 100 times the height of 12.
- 00:51
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, [Explanation for calculating the volume of 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. [Explanation for calculating the volume of a 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... [Explanation for calculating the volume of a Cone]
- 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. [Explanation for calculating the volume of a Cone]
- 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... [Explanation for calculating the volume of a Cone]
- 01:34
1/3 times pi times 10 squared times height....equals 1/3 times pi times 100 times 12.
- 01:47
1200 divided by 3 equals 400...so our answer is....400 pi. [Explanation for calculating the volume of a Cone]
- 01:54
Since 400 pi is bigger than 400...looks like Pharaoh Irving is really going to be the one
- 02:00
living [Comparison of the volume of pyramid and cone]
- 02:11
the good... afterlife.
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