10.
\includegraphics[max width=\textwidth, alt={}]{a202ddae-5ecd-4803-9a05-33c37d1880cd-10_597_533_155_760}
The diagram above shows a closed box used by a shop for packing pieces of cake. The box is a right prism of height h cm . The cross section is a sector of a circle. The sector has radius r cm and angle 1 radian.
The volume of the box is \(300 \mathrm {~cm} ^ { 3 }\)
a) Show that the surface area of the box, \(S \mathrm {~cm} ^ { 2 }\), is given by
$$S = r ^ { 2 } + \frac { 1800 } { r }$$
b) Hence find the value of \(r\) and the value of \(h\) which minimises the surface area of the box.