If there is a cylinder, and a cone inside the cylinder, shouldn’t one “empty space” on either side of the cone, be half the volume of the cone? It has the same height, radius, etc. Of a cone. So shouldn’t the equation for half a cone be 1/2 ( 1/3πr^2). Then meaning that both the halves equal one, and that a cylinder is equal to two cones instead of three??? I just don’t understand conceptually how they aren’t equal. Where is that third cone going?? Does it have something to do with it being 3D??? I’m not stupid I swear I just can’t visualize it😭
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It’s a Calculus thing. Going from a square to a cube is going from X^(2) to X^(3) . One of the rules of calculus is that exponents become coefficients. so X^(2) becomes 2X and X^(3) becomes 3X^(2) .
If you want to think about it more spacially, remember that area goes up expodentially with radius. A circle with a radius of 1″ has about 3.142 square inches while a circle with a radius of 2 has about 12.5 square inches of radius.
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