In solving a, we must get the formula needed then substitute
the given so we have
A=πr2
dA/dt=1,400 km2/s
then solve for dA/dt
<span>1400</span><span> <span>k<span>m2</span>/</span></span><span>s=2<span>π(</span><span>8000</span></span><span> <span>km</span>)<span><span>dr</span><span>/dt</span></span></span>
<span>
<span>dr</span><span>dt</span>≈<span>0.028</span><span> <span>km</span>/</span>s
</span>
In solving b,
its just the same as solving the letter a, the only difference is that the
radius is not given so we get the formula for A, then substitute
<span>640</span>,<span>000</span> k=<span>π<span>r2</span>⟹</span>r≈<span>451.352</span> <span>km</span>
Then solve for
dAdt
1,<span>400</span><span> <span>k<span>m2</span>/</span></span><span>s=2<span>π(</span><span>451.352</span></span><span> <span>km</span>)<span><span><span>dr</span><span>dt</span></span>⟹</span><span><span><span>dr</span><span>dt</span></span>≈</span><span>0.494</span></span><span> <span>km</span>/</span><span>s</span>
