Volume of Solid of Revolution Around X-axis
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This example demonstrates the volume of a solid of revolution around the X-axis. Key mathematical concepts include the formula for calculating the volume of a solid of revolution. Using GeoGebra commands such as Rotate, Cylinder, and Integral, the formation process of the solid can be dynamically shown. Suitable for high school mathematics education and learning.
GeoGebra Commands & Parameters
Point(xAxis) → APoint(xAxis) → CTextfield(f) → inputBox1Textfield(A) → inputBox2Textfield(C) → inputBox3Textfield(C) → inputBox4Textfield(C) → inputBox5Segment(A, (x(A), f(x(A)))) → cSegment(C, (x(C), f(x(C)))) → aCircumcircleArc((x(A), f(x(A)), 0), (x(A), (f(x(A)) * cos(rotasi / 2)), (f(x(A)) * sin(rotasi / 2))), (x(A), (f(x(A)) * cos(rotasi)), (f(x(A)) * sin(rotasi)))) → dCircumcircleArc((x(C), f(x(C)), 0), (x(C), (f(x(C)) * cos(rotasi / 2)), (f(x(C)) * sin(rotasi / 2))), (x(C), (f(x(C)) * cos(rotasi)), (f(x(C)) * sin(rotasi)))) → eSegment(C, (x(C), (f(x(C)) * cos(rotasi)), (f(x(C)) * sin(rotasi)))) → bSegment(A, (x(A), (f(x(A)) * cos(rotasi)), (f(x(A)) * sin(rotasi)))) → iRotate(g, rotasi, xAxis) → g_1Textfield(rotasi) → inputBox6Sequence(Rotate[g, b, xAxis], b, 0, rotasi, rotasi / garis) → list2Sequence(CircumcircleArc[(b, f(b), 0), (b, (f(b) * cos(rotasi / 2)), (f(b) * sin(rotasi / 2))), (b, (f(b) * cos(rotasi)), (f(b) * sin(rotasi)))], b, x(A), x(C), (x(C) - x(A)) / partisi) → list1Cylinder((x(B), 0, 0), (x(B) + h, 0, 0), f(x(B) + h)) → v, r, c_1, oPolygon((x(B), 0), (x(B) + (x(C) - x(A)) / partisi, 0), (x(B) + (x(C) - x(A)) / partisi, f(x(B) + h)), (x(B), f(x(B) + h))) → poly2, q, s, t, a_1Integral(f, x(A), x(C)) → lSequence(Cylinder[(x(A) + (i * h), 0, 0), (x(A) + ((i + 1) * h), 0, 0), f(x(A + h) + (h * i))], i, 0, partisi - 1) → list3Surface(a, (f(a) * cos(b)), (f(a) * sin(b)), a, x(A), x(C), b, 0, rotasi) → kIntersect(t, a_1) → DIntersect(s, t) → EMidpoint(D, E) → F
AI Drawing Prompt Reference
Draw a solid of revolution around the x-axis to demonstrate the volume calculation process. Rotate a curve segment to form the surface of the solid, simulate volume elements with cylinders, and compute the volume using integration. Dynamically show the rotation process, label key points and the integral interval, highlighting the geometric meaning of the solid's volume and the method of integral calculation.
The prompt above was compiled from the original drawing commands and is for reference only.