Higher November 2022 Unit 1 Q16
16. A cone and a cylinder have equal volumes.
The cone has a base radius of \(r\) cm and a height of \(h\) cm.
The cylinder has a base radius of \(r\) cm and a height of \(\dfrac{3}{2}r\) cm.
Find \(h\) in terms of \(r\).
You must express your answer in its simplest form. [3]
From the formula list: Volume of cone \(= \dfrac{1}{3}\pi r^2 h\)
| Scheme | Marks | Comments |
|---|---|---|
| \(\left(\dfrac{1}{3}\pi r^2 h =\right)\; \pi r^2 \times \dfrac{3r}{2}\) or equivalent | M1 | Correct expression for volume of cylinder |
| \(2\pi r^2 h = 3\pi r^2 \times 3r\) or equivalent OR \(\dfrac{1}{3}h = \dfrac{3r}{2}\) or equivalent OR \(h = \dfrac{3\pi r^2 \times 3r}{2\pi r^2}\) or equivalent | M1 | Equating volumes AND one further step to find \(h\) e.g.
|
| \(h = \dfrac{9r}{2}\) or equivalent | A1 | Correct simplified expression. Award full marks for a correct answer, provided no incorrect working seen. |