PLease show all your work please!

PROBLEM $1(20$ points$)$

A spherical tank $($partially filled with water$)$ leaks through a hole at the bottom of the tank. Water is flowing out at a flow rate that can be estimated using the following first$-$order ordinary differential equation:

$\frac{dV}{dt}(\frac{m^3}{sec})=-0\mathrm{.}0017224\sqrt[\phantom{2}]{H(m)}$

Where,

$H$ is the height of the water in the spherical tank $($ m $)$

$\frac{dV}{dt}$ is the flow rate $(\frac{m^3}{sec})$ or the change in the volume of the water in the spherical tank with respect to time.

$V$ is the volume of the water in the spherical tank $(m^3)=(\frac{3}{2}{H}^2-\frac{1}{3}{H}^3)$

Use the $4^{th}-$order RK method with a step size of $120$ seconds. $(t=$ time $=120sec.)$ to estimate the height of the water $(H)$ in the tank after $240$ seconds due to leakage knowing that the initial height of water in the tank is $2\mathrm{.}75$ m $.$