4MA0 Higher January 2015 Paper 4 Q21
21 The diagram shows a cylinder and a sphere.
Diagram NOT accurately drawn
The cylinder has radius \(r\) cm and height \(h\) cm.
The sphere has radius \(2r\) cm.
The volume of the cylinder is equal to the volume of the sphere.
Find an expression for \(h\) in terms of \(r\).
Give your answer in its simplest form.
(3)
| Scheme | Marks |
|---|---|
| \(\dfrac{4}{3} \times \pi \times (2r)^3\) | M1 |
| \(\pi \times r^2 \times h = \dfrac{4}{3} \times \pi \times (2r)^3\) | M1 |
| \(\dfrac{32}{3}r\) | A1 |
| (3 marks) |
Notes
M1: condone omission of brackets
M1: dep
brackets must be present or \(8r^3\) seen