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A balloon, which always remains spherical, has a variable diameter `3/2(2x+1)`.Find the rate of change of its volume with respect to x. |
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Answer» `d=3/2(2z+1)` `dv/dx=?,v=4/3pix^3=pi/6d^3` `(d(pi/6)d^3)/dx=pi/6(d(d^3))/dx` `=pi/6(d(d^3))/d (d(d))/dx` `=pi/63d^2(d(3/2)(2x+1))/dx` `=(pi/2 3/2d^2)(d2x+1)/dx` `=((3pid^2)/4)2` `=(3pi)/2d^2` `=3/2pi(3/2(2x+1))^2` |
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