Unit 3 IB Review Questions
IB HL1 Apps and Interpretation
1. Helen is building a cabin using cylindrical logs of length 2.4 m and radius 8.4 cm. A wedge
is cut from one log and the cross-section of this log is illustrated in the following diagram.
a) [4 marks] Find the volume of this log.
b) [5 marks] Find the surface area of this log.
2. In the Voronoi diagram below, the sites A (3,6), B (-2,-4), and C (10,-4) are given along
with dashed lines of the edges. The diagram is bounded by the lines 𝑦 = 10, 𝑦 = −6,
𝑥 = 12 and 𝑥 = −8.
a) [6 marks] Find the equation of edge between sites A and C
b) [1 mark] Find the equation of edge between sites B and C
c) [4 marks] Add Site D (-4,6) to the diagram, and sketch a new Voronoi diagram with
solid lines for all edges. Any lines that are left as dashed lines will not be considered
a part of the new diagram.
3. On the terrain map shown, the grid units are kilometers. The hiker is at a viewing
platform H, 400 m above the base camp O.
a) [1 mark] State the 3-dimensional coordinate of the hiker (in meters)
b) [2 marks] How far is the hiker from base camp?
c) From the viewing platform, the hiker can see the summit of a mountain at M. The
mountain top is 500 meters above the base camp level.
i.
[1 mark] Find the 3-dimensional coordinate of the mountain top in meters.
ii.
[3 marks] Which is closer to the base camp, the hiker or the summit of the
mountain at M (show your work)?