Answer:
Step-by-step explanation:
Given
Volume of spherical Balloon is given by
[tex]V=\frac{4}{3}\pi r^3[/tex]
(a)Rate of change of balloon w.r.t to radius is given by
[tex]\frac{\mathrm{d} V}{\mathrm{d} r}=3\times \frac{4}{3}\pi r^2=4\pi r^2[/tex]
at [tex]r=9\ in.[/tex]
[tex]\frac{\mathrm{d} V}{\mathrm{d} r}=324\pi\ in.^2[/tex]
(b)Using the rate Volume change when radius increases from r=9 in. to r=9.5 in.
[tex]\Delta V=4\pi (9)^2(9.5-9)=162\pi\ in.^3[/tex]
