Volumes of Solids - Disk & Washer Method

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2020-04-22 03:00

This example demonstrates calculating volumes of solids using the disk and washer methods. It involves core calculus concepts like integration, rotating function graphs, and volume computation. Constructed with GeoGebra commands like Textfield, Vector, IntegralBetween, Surface, Sequence, and objects such as xa, xb, f, g. Suitable for high school students and calculus learners.

GeoGebra Commands & Parameters

Textfield(f) → InpF
Vector((xc, 0, 0), (xc, f(xc), 0)) → RfVec
Textfield(g) → InpG
IntegralBetween(f, g, xa, xb) → BaseRegion
Vector((xc, 0, 0), (xc, g(xc), 0)) → RgVec
Surface(If[xa ≤ x ≤ xb, f(x)], (2 * π), kline) → FSurf
Surface(If[xa ≤ x ≤ xb, g], (2 * π), kline) → GSurf
Surface(u, ((((1000 * (g(u + 0.001) - f(u))) * (u - xc)) + f(u) - k) * cos(v)) + k, ((((1000 * (g(u + 0.001) - f(u))) * (u - xc)) + f(u) - k) * sin(v)), u, xc, xc + 0.001, v, 0, revolve) → Washer
Sequence(Surface[u, ((((1000 * (g(u + 0.001) - f(u))) * (u - ((i * dx) + xa))) + f(u) - k) * cos(v)) + k, ((((1000 * (g(u + 0.001) - f(u))) * (u - ((i * dx) + xa))) + f(u) - k) * sin(v)), u, (i * dx) + xa, (i * dx) + xa + 0.001, v, 0, revolve], i, 0, n, 1) → RfSolid
Textfield(xa) → InpA
Textfield(xb) → InpB

AI Drawing Prompt Reference

Draw a rotating solid of two function graphs to demonstrate the disk and washer methods for calculating volumes. Include the integral region between the functions, vectors for the rotation axis, and surfaces generated by rotating the function graphs. Show the volume calculation using the washer method. Start by plotting the base region and the two function graphs, then generate the surfaces of revolution, and finally represent the volume calculation with the washer method.

The prompt above was compiled from the original drawing commands and is for reference only.