frac{4}{3}\pi(r-3)^3 .$$ We
    wanted to approximate the volume if $r=3.2$, so our change in
    $r$ is $dr=3.2-3=0.2$. We can rewrite our polynomial as
    $$P(r)=36\pi+36\pi(dr)+12\pi(dr)^2+\frac{4}{3}\pi(dr)^3.$$ We
    are now prepared to approximate the volume using a first,
    second, and third order approximation.</p>

    <ol>
      <li>A first order approximation yields $P=36\pi+ 36\pi\cdot
      0.02 =36.72\pi.$ The volume increased by $0.72\pi$
      m$^3$.</li>

      <li>A second order approx