(Solved): The volume of a cylinder of radius \( r \) and height \( h \) is \( V=\pi r^{ ...

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The volume of a cylinder of radius \( r \) and height \( h \) is \( V=\pi r^{2} h \). Calculate the percentage increase in \( V \) if \( r \) is increased by \( 0.6 \% \) and \( h \) is increased by \( 3 \% \). Hint: Use the linear approximation to show that \( \frac{\Delta V}{V} \approx \frac{2 \Delta r}{r}+\frac{\Delta h}{h} \) \( \frac{\Delta V}{V} \times 100 \%= \) \( \% \) The volume of a certain cylinder \( V \) is determined by measuring \( r \) and \( h \). Which will lead to a greater error in \( V \) : A. a \( 1 \% \) error in \( r \) is equivalent to a \( 1 \% \) error in \( h \) B. a \( 1 \% \) error in \( r \) C. a \( 1 \% \) error in \( h \)