Question #f0ea3

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Question #f0ea3

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Answer 1 · 2017-11-09T18:15:55

$\frac{1024 π}{625}$ $(1024pi)/625$

Explanation:

The region bounded by the given curves has been shown in the attached figure in red shade. Now consider an elementary strip of width $δ x$ $delta x$ shown in blue pen in the figure. Its length would be $y = 16 - (16 - x^{2}) = x^{2}$ $y= 16-(16-x^2) = x^2$ . If this strip is revolved around y=16, the volume of the elementary disc so formed would be $π {(x^{2})}^{2} δ x$ $pi (x^2)^2 delta x$

The volume of the solid so generated would be $\int_{x = o}^{4} π x^{4} d x$ $int_(x=o)^4 pi x^4 dx$

= $π {(\frac{x^{5}}{5})}^{4} = \frac{1024 π}{625}$ $pi (x^5 /5)^4 = (1024pi)/625$
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