Case study·Hard exam skill (4/5)·No calculator
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Question
An ice-cream model is made from a cone of radius and height , topped by a hemisphere of the same radius. The circular face where the cone and hemisphere touch is not exposed.
Total: 5 marks
(a) Find the slant height of the cone. (1 mark)
(b) Find the volume of the cone in terms of . (1 mark)
(c) Find the total volume of the cone and hemisphere. (1 mark)
(d) Find the exposed outer surface area of the model in terms of . (2 marks)
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