2.47: Optimising the surface area of a cylinder

0606/22/O/N/17 — Question 6 · 8 marks

The volume of a closed cylinder of base radius

x\text{ cm}

and height

h\text{ cm}

500\text{ cm}^{3}

(i)

Express

h

in terms of

x

[1]

(ii)

Show that the total surface area of the cylinder is given by

A = 2\pi x^{2} + \dfrac{1000}{x}\text{ cm}^{2}

[2]

(iii)

Given that

x

can vary, find the stationary value of

A

and show that this value is a minimum.

[5]