A balloon, which always remains spherical, has a variable diameter 23(2x+1).Find the rate of change of its volume with respect to x.

Solution: d=23(2z+1)ddxv=?,v=34πx3=6πd3dxd(6π)d3=6πdxd(d3)=6πdd(d3)dxd(d)=63πd2dxd(23)(2x+1)=(2π23d2)dxd2x+1=(43πd2)2=23πd2=23π(23(2x+1))2

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A balloon, which always remains spherical, has a variable diam

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

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A balloon, which always remains spherical, has a variable diameter

\frac{3}{2} (2 x + 1)

.Find the rate of change of its volume with respect to x.

5 mins ago

Discuss this question LIVE

5 mins ago

Solution:

d = \frac{3}{2} (2 z + 1)

d \frac{v}{d x} = ?, v = \frac{4}{3} π x^{3} = \frac{π}{6} d^{3}

\frac{d ( \frac{π}{6} ) d ^{3}}{d x} = \frac{π}{6} \frac{d ( d ^{3} )}{d x}

= \frac{π}{6} \frac{d ( d ^{3} )}{d} \frac{d ( d )}{d x}

= \frac{π}{63} d^{2} \frac{d ( \frac{3}{2} ) ( 2 x + 1 )}{d x}

= (\frac{π}{2} \frac{3}{2} d^{2}) \frac{d 2 x + 1}{d x}

= (\frac{3 π d ^{2}}{4}) 2

= \frac{3 π}{2} d^{2}

= \frac{3}{2} π (\frac{3}{2} (2 x + 1))^{2}

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Question Text	A balloon, which always remains spherical, has a variable diameter $\frac{3}{2} (2 x + 1)$ .Find the rate of change of its volume with respect to x.
Answer Type	Text solution:1
Upvotes	150