(Solved): The volume of a cone is given by \( V=\frac{1}{3} \pi r^{2} h \), where \( h \) is the height of t ...

The volume of a cone is given by \( V=\frac{1}{3} \pi r^{2} h \), where \( h \) is the height of the cone and \( r \) is the radius of the circular base. A cone has a height of \( 8 \mathrm{~cm} \). If the radius is increased from \( 10 \mathrm{~cm} \). to \( 10.2 \mathrm{~cm} \). a) Find the exact change \( (\Delta V) \) in the volume of the cone. \( \Delta V= \) b) Find the approximate change \( (d V) \) in the volume using differentials. \( d V= \) Note: to be sure that your answers are graded correctly, either enter a mathematical expression for each quantity, or enter each answer to at least 8 decimal places.