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Other Shapes (with Circles)

By Tomi Chen

Spheres

Spheres. A sphere is basically a 3D circle and has the interesting property being the same height no matter how you position it, in other words, it is a shape of constant width. Because of this, they make great bearings or when you need to roll something in any direction. However, the way to find the area or volume of a sphere may not be so obvious. We will have to look it up, or you could reinvent math on your own. I opted for the former. The formula for a sphere's surface area suprised me. It is 4*pi*r2. This may be familiar, it's just 4 times the formula for the area of a circle. I have no idea why this is, so if you have answers, please tell me. How? You figure that out. Anyway, the formula for volume is 4/3(pi*r3). By the way, r is the radius, or half the width of the sphere. I'll just assume you know what pi is. If you don't, look near the end.

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sphere picture

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Cylinders

Cylinders are basically circles that have decided that 2D is too boring. Instead of turning into a sphere, they become longer, making a cylinder. Cylinders are pretty common, it's probably the shape of your water bottle, toilet paper roll, or just any rolled up object. (If your toilet paper is not a cylinder shape, please send a picture.) The way to find the surface area and volume of a cylinder is more obvious, for surface area it's (2*pi*r2)+(2*r*pi*h), and for volume it's pi*r2*h. In other words, for surface area, it's the top plus the bottom, plus the circumfrence times height, and for volume it's the base area times height.

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cylinder picture

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Cones

Cones are another pretty common sight. They might not be as common as cylinders or spheres, but still pretty common. Party hats are a great example of a cone. A cone is a shape with a circle base that slowly tapers to a point. Again, the formulas may not be too apparent, so here they are. Surface area is (pi*r*s)+(pi*r2) where r is the radius and s is the slant height. If you only have the radius and the height, you can solve for the slant height with Pythagoras' Theorem, making the formula (pi*r*(sqrt(h2+r2))+(pi*r2). The formula for volume is much simpler, just 1/3(pi*r2*h). That's right, the volume of a cone is just 1/3 the volume of the cylinder with the same base area.

Try It! (Surface Area)

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cone picture

Try It! (Volume)

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Great Job! You're practically an expert!

Well, maybe not yet. Pi is a Greek letter that in mathamatics, is a constant. It is the ratio of a circle's circumfrence to it's diameter. Pi is irrational, which means it cannot be written as a ratio of 2 numbers. Pi is also transendental, which is something I probably shouldn't get to here. Anyways, check out more here.