A) \[27\pi {{(2x+3)}^{2}}\]
B) \[\frac{27\pi }{16}{{(2x+3)}^{2}}\]
C) \[\frac{27\pi }{8}{{(2x+3)}^{2}}\]
D) None of these
Correct Answer: C
Solution :
Radius of balloon =\[r=\frac{3}{4}(2x+3)\Rightarrow \frac{dr}{dx}=\frac{3}{2}\] \[\therefore \]Rate of change in volume = \[4\pi {{\left( \frac{3}{4} \right)}^{2}}{{(2x+3)}^{2}}.\frac{3}{2}\] \[=\frac{27\pi }{8}{{(2x+3)}^{2}}\].
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