3.1 Three-dimensional geometryIB Maths: Applications and Interpretation SL: Mind map

Exam questions on 3.1 Three-dimensional geometry

1. The points $P(2,-1,4)$ and $Q(8,3,-8)$ lie in three-dimensional space, with all lengths in metres.
   The point $R$ is such that $Q$ is the midpoint of $[PR]$. Find the coordinates of $R$.2 marks
2. A toy is made from a solid hemisphere of radius 6 cm and a solid cone of base radius 6 cm and vertical height 8 cm. The base of the cone is fixed exactly onto the flat circular face of the hemisphere.
   Find the angle between the slant height of the cone and its circular base.2 marks
3. A tent is in the shape of a right pyramid with square base $ABCD$ of side 6 m. The vertex $V$ is vertically above the centre $M$ of the base, and $VM=4$ m.
   Find the length of the edge $VA$.3 marks