Volumes of Pyramids and Cones old
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.
|Area and Volume||Volume|
The volume of a pyramid is one-third the volume of the prism with the same base.
Because we have a square base, we know that its area is length times width, which is just
100 meters squared.
We plug that into our formula and solve for the volume. One-third times 100 times the
height of 12. 100 times 12 equals 1200, divided by 3 equals 400.
His neighbor, Pharaoh Irving, is going to meet his maker in a cone rather a pyramid,
so he'll have to use the formula one-third...pi times radius squared times height to find
the volume of the cone.
If we look closely at the volume formula of a cone, it looks a lot like the volume formula
of a pyramid...
...since pi times radius squared is the area of a circle, which is the shape of a cone's
base...and B is the area of the base of a pyramid.
If the radius of the cone's base is 10 and the height is 12, we can plug them into our
1/3 times pi times 10 squared times height....equals 1/3 times pi times 100 times 12. 1200 divided
by 3 equals 400...so our answer is....400 pi.
Since 400 pi is bigger than 400...looks like Pharaoh Irving is really going to be the one
the good... afterlife.