Long answer·Challenge (5/5)·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
A solid is formed by fixing a hemisphere of radius cm on a cylinder of the same radius. Its outer curved surface area, excluding the bottom base, is cm. Find the height of the cylinder and then find the volume of the solid. Take .
Total: 6 marks
(a) Find the height of the cylinder. (3 marks)
(b) Find the volume of the solid. (3 marks)
Something wrong with this item?