9 a a cuboid has a total surface area of 150 cm and is such that its b

Question

9. (a) A cuboid has a total surface area of 150 cm² and is such that its base
is a square of side x cm. Let the height of the cuboid be h cm. Express
h in terms of z. Express the volume, V cm³, of the cuboid in terms of
x. Hence, determine, as x varies, its maximum volume and show that
this volume is a maximum.
(b) The volume of a solid right circular cylinder of radius r cm is 432
cm³. Let S cm² be the total surface area of the cylinder. Express S in
terms of r. Calculate the value of r for which S has a stationary value.
Determine whether this value of r makes the surface area a maximum
or a minimum, and find the corresponding value of the height of the
cylinder.