To find the volume of a sphere of radius R, the cross sections are Therefore If the sphere is centred at the origin, then x 0. -Bun Therefore V Consider the intersection of the sphere and the xy-plane. Its shape is a circle. Let (xo, yo) be the point on the circle above the x-axis, at a given x-value xo. Then the points (0, 0), (xo, 0), and (xo, yo) form a triangle. or yo A(x) dx. The hypotenuse has length or This is the radius of the cross section, so A(x) = Then V = dx.
To find the volume of a sphere of radius R, the cross sections are Therefore If the sphere is centred at the origin, then x 0. -Bun Therefore V Consider the intersection of the sphere and the xy-plane. Its shape is a circle. Let (xo, yo) be the point on the circle above the x-axis, at a given x-value xo. Then the points (0, 0), (xo, 0), and (xo, yo) form a triangle. or yo A(x) dx. The hypotenuse has length or This is the radius of the cross section, so A(x) = Then V = dx.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:To find the volume of a sphere of radius R, the cross sections are
Therefore
If the sphere is centred at the origin, then € 0.
-LA)
=
Consider the intersection of the sphere and the xy-plane. Its shape is a circle. Let (xo, Yo) be the point on
the circle above the x-axis, at a given x-value xo. Then the points (0, 0), (xo, 0), and (xo, yo) form a
triangle.
Therefore V
or yo
A(x) dx.
The hypotenuse has length or
This is the radius of the cross section, so A(x) =
Then V =
dx.
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