The volume of a sphere with radius r is definitively calculated using the formula V = (4/3)πr3. The discussion clarifies that the volume is derived through calculus and integration, specifically by considering the cross-sectional area of disks oriented vertically. Each disk's volume is determined by multiplying its area by its thickness, dx. This method effectively illustrates how integration is applied to derive the volume of a sphere.
PREREQUISITESStudents studying calculus, educators teaching integration techniques, and anyone interested in the geometric applications of calculus in determining volumes of three-dimensional shapes.
Probably a typo - the volume is (4/3)##\pi r^3##.Feodalherren said:
The book is using disks that are oriented vertically (the x-axis intersects each disk perpendicularly). The volume of such a disk is its area times its thickness, dx.Feodalherren said:Homework Equations
calculus, integration
The Attempt at a Solution
I have the solution in the book but it's confusing me, I'll attach a picture.
So I get lost where it starts talking about a cross-sectional area all of a sudden multiplying by ∏. What's going on here?!