A sector of angle 120° is removed from a thin circular metal sheet of radius 14cm. The remaining net is folded to form a right circular cone. Calculate and correct to three significant figures: (i) the curved outer surface; (ii) the height of the cone; (iii) the volume of the cone.

Use your graph to find

The least value of a parabola $y = ax^2 + bx + c$ occurs at its vertex. The x-coordinate of the vertex is $x = -\frac{b}{2a}$.
For $y = x^2 - 4x - 21$, $a=1$ and $b=-4$.

From the table, when $x=2$, $y = -25$. This is the lowest point on the graph.
The least value of the relation is $\boxed{-25}$.

The axis of symmetry is a vertical line that passes through the vertex of the parabola. Its equation is $x = -\frac{b}{2a}$.
From the calculation in (i), the x-coordinate of the vertex is $x=2$.
The equation of the axis of symmetry is $\boxed{x=2}$.

To find the truth set using the graph of $y = x^2 - 4x - 21$, we can rewrite the equation $x^2 - 4x - 16 = 0$ as $x^2 - 4x - 21 + 5 = 0$.
This means $y + 5 = 0$, or $y = -5$.
On your graph, draw a horizontal line at $y = -5$. The truth set consists of the x-coordinates where this line intersects the parabola $y = x^2 - 4x - 21$.
Reading from the graph, the approximate points of intersection are:
$x \approx -2.5$ and $x \approx 6.5$.
(For verification, using the quadratic formula $x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-16)}}{2(1)} = \frac{4 \pm \sqrt{16+64}}{2} = \frac{4 \pm \sqrt{80}}{2} = \frac{4 \pm 4\sqrt{5}}{2} = 2 \pm 2\sqrt{5}$.
$2 + 2\sqrt{5} \approx 2 + 2(2.236) = 2 + 4.472 = 6.472$.
$2 - 2\sqrt{5} \approx 2 - 2(2.236) = 2 - 4.472 = -2.472$.)
The truth set is approximately $\boxed{\{-2.5, 6.5\}}$.