3)+a_2(r-3)^2+a_3(r-3)^3,$$ whose derivatives
    are $$P'=a_1+2a_2(r-3)+3a_3(r-3)^2, P''=2a_2+6a_3(r-3),
    P'''=6a_3.$$ So that the derivatives of the volume function
    match the derivatives of the polynomial (at $r=3$), we need to
    satisfy the equations in the table below.</p>

    <table>
<tr><th> $k$ </th><th> Value of $V$ at the $k$th derivative </th><th> Value of $P$ at the $k$th derivative </th><th> Equation</th></tr>
<tr><td>  $0$ </td><td> $V(3) = \frac{4}{3}\pi (3)^3 = 36\pi$ </td><td> $P(3