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  • A balloon, which always remains spherical, has a variable diameter3 by 2 2 x plus 1 Find the rate of change of its volume with respect to x.

13) A balloon, which always remains spherical, has a variable diameter \frac{3}{2}( 2x +1) Find the rate of change of its volume with respect to x.

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Volume of sphere(V) = \frac{4}{3}\pi r^{3}
Diameter = \frac{3}{2}(2x+1)
So, radius(r) = \frac{3}{4}(2x+1)
\frac{dV}{dx} = \frac{d(\frac{4}{3}\pi r^{3})}{dx} = \frac{d(\frac{4}{3}\pi (\frac{3}{4}(2x+1))^{3})}{dx} = \frac{4}{3}\pi\times 3\times\frac{27}{64}(2x+1)^{2}\times 2
                                                                               = \frac{27}{8}\pi (2x+1)^{2}

Posted by

Gautam harsolia

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