Question

A water tank consist of a cylindrical part of radius $r$ and height $h,$ and a hemispherical top. The tank is to be constructed to hold $500m^3$ of fluid when filled. The surface area of the cylindrical part is $2nrh,$ and its volume is $n{r}^{2}h.$ The surface area of the hemispherical top is given by $2n{r}^2,$ and its volume is given by $2n\frac{r^3}{3}.$ The cost to construct the cylindrical part of the tank is $RM\frac{250}{m^2}$ of surface area; the hemispherical part costs RM$350/$m ${?}^2.$ Plot the cost versus $r$ for $2r10m,$ and determine the radius that results in the least cost. Compute the corresponding height $h.$

Use Matlab$/$Octave to get the answers and submit the Matlab script along with your answers, relevant plots and discussion via UTM eLearning.$$