Application of DerivativeMedium

Question

A balloon, which always remains spherical, has a variable diametre 3/2 (2x + 3). The rate of change of volume with respect to x will be-

Options

A. (2x - 3)2
B. (2x + 3)2
C. (3x + 2)2
D. (3x - 2)2

Solution

Given        Diameter = 2r = (2x + 3)
r = (2x + 3)     
v = πr3
π × 3r2 ×
= π × 3 × (2x + 3)2  ×
(2x + 3)2

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