Curiosity about infinity in geometry(Not homework just curious)

by caters
Tags: area, curiosity, curious, geometry, geometrynot, homework, infinity, volume
caters is offline
Feb22-14, 11:34 PM
P: 26
Okay, let's say you have an infinitely long line segment.

Using area and volume formulas for different shapes, would you get an infinitely large shape that the formula was for in the first place?
For rectangles, would you get an infinitely large rectangle with A = l * w?
What about triangles with 1/2 * b * h?
What about squares with l^2
what about rombi with A = b * h?
what about trapezoids with A = ((b1 + b2)*h)/2?
what about pentagons with A = 5/2 * l * a(apothem)?
hexagons with A = (3√3 s2)/ 2?
what about other regular polygons with Area = (a(apothem) x p(perimeter))/2?
what about ellipses with π * vertical radius * horizontal radius?
What about circles with π * r^2
What about spheres with V = ⁴⁄₃πr?
What about triangular prisms with 1/2 x b x h x l?
what about other prisms with V = area of base * l (yes that includes the cylinder at the infinite end)?
what about dodecahedrons with (15+7√5)/4 (Edge Length)^3
what about octahedrons with (√2)/3 (Edge Length)^3
what about Icosahedrons with 5(3+√5)/12 (Edge Length)^3
What about toruses that have holes with 2 π^2 R(radius of hole) r^2(radius of circular cross section)?
What about cones with π r^2 (h/3)?
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SteamKing is offline
Feb23-14, 02:47 AM
HW Helper
P: 5,549
What do you think?
caters is offline
Feb23-14, 03:01 PM
P: 26
I think that you would get an infinitely large shape from an infinitely long line segment but I honestly don't know.

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