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प्रश्न
Find the volume of a solid obtained by the complete revolution of the ellipse `x^2/36 + y^2/25 = 1` about X-axis.
उत्तर
From the equation of the ellipse
`x^2/36 + y^2/25 = 1`
`y^2 = 25/36 (36 - x^2)`
Lel V be the required volume of the solid obtained by revolving the ellipse about major axis i.e. X-axis.
V = `pi∫_-6^6 y^2` dx
= `∫_-6^6 25/36(36 - x^2)` dx
= `(25pi)/36 .2 ∫_-6^6 (36 - x^2)` dx ....(by property)
= `(25pi)/18 [36x - x^3/3]_0^6`
= `(25pi)/18 [36(6) - 6^3/3 - 0]`
= `(25pi)/18[144]`
V = 200π cubic units.
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