what is the formula for the volume of a sphere
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volume of the sphere is given by  V = 4/3Pi r^3


Find the volume formed by revolving the circle given by r^2 = x^2 + y^2 about the x-axis

usig disk method

limits are [r,-r].............. where r = radius

from  V=pi ∫R(x)^2 dx

given r^2 = y^2 + x^2....................x = {r^2 - y^2}^1/2

V = pi ∫({r^2 - y^2}^1/2) dy

V = pi ∫(r^2 - y^2) dy ....... [r,-r]

V = pi(yr^2 - y^3/3) .......... [r,-r]

V = pi{ (r^3 - r^3/3) - (-r^3 + r^3/3) }

V = pi(2/3r^3 + 2/3r^3)

V = pi(4/3r^3)

V = 4/3pir^3,............ "hence proved"

by Level 3 User (4k points)

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