2.70: Optimising the volume of a conical tent

0606/23/O/N/16 — Question 7 · 9 marks

In this question all lengths are in metres.

A conical tent is to be made with height

h

, base radius

r

and slant height

0.5h + 2

, as shown in the diagram.

(i)

Show that

r^{2} = 2h + 4 - 0.75h^{2}

[2]

(ii)

The volume of the tent,

V

, is given by

\dfrac{1}{3}\pi r^{2}h

. Given that

h

can vary find, correct to

2

decimal places, the value of

h

which gives a stationary value of

V

[5]

(iii)

Determine the nature of this stationary value.

[2]