IB Maths AA HL Sl 3 1 Three Dimensional Geometry Questions

Practise finding 3D distances, midpoints, lengths, angles, volumes and surface areas from coordinates or solid diagrams using geometry and correct units.

Exam points

Use three-dimensional coordinates to calculate distances and midpoints between points, showing the coordinate differences and resulting exact or numerical value.
Find lengths, angles, volumes or surface areas in three-dimensional solids by identifying right-angled triangles and applying the appropriate geometric formula.

[Maximum number: 3]

The points A and B lie on a circle, with centre O and radius 19.5 cm , such that $\mathrm{BO} \widehat{\mathrm{O}}=210^{\circ}$ .
A piece of paper is cut into the shape of the sector BOA .
A hollow cone with no base is constructed from the sector by joining the points A and B . The sector forms the curved surface of the cone.
This is shown in the following diagrams.

Figure for Question IB Maths AA HL Sl 3 1 Three Dimensional Geometry Questions question 1 — IB Maths AA HL

Find

the radius of the cone.

EITHER
arc length $=19.5\left(\frac{7 \pi}{6}\right)$ OR $=\frac{210}{360}(2 \pi(19.5))\left(=\frac{91 \pi}{4}=71.4712 \ldots\right)$
attempt to set $2 \pi r$ equal to arc length
$2 \pi r=71.4712 \ldots$

OR
attempt to set $\pi r l$ equal to their area from (a)
$19.5 \pi r=696.844 \ldots$

THEN
$r=11.4\left(=\frac{91}{8}=11.375\right)(\mathrm{cm})$

All question bank results loaded

IB Maths AA HL Sl 3 1 Three Dimensional Geometry Questions question 1