initial volume of balloon =
[tex] \frac{4}{3} \times \frac{22}{7} \times r^{3} \\ \frac{4}{3} \times \frac{22}{7} \times {3}^{3} \\ 113.14[/tex]
so intial volume is 113.14 cubic inches
volume after one hour will be 113.14 - 2 = 111.14 inches
new radius
[tex]111.14 = \frac{4}{3} \times \frac{22}{7} \times {x}^{3} \\ \frac{2333.94}{88} = {x}^{3} \\ 26.52 = {x}^{3} \\ x = 2.98[/tex]
Rate change of radius is
[tex] \frac{2.98}{3} \times 100 \\ \frac{298}{3} \\ 99.93\%[/tex]
Rate change is 0.7% per hour the radius is decreasing
