1MA0 Higher June 2012 Paper 1 Q25
25 The diagram shows a solid metal cylinder.
Diagram NOT accurately drawn
The cylinder has base radius \(2x\) and height \(9x\).
The cylinder is melted down and made into a sphere of radius \(r\).
Find an expression for \(r\) in terms of \(x\). (3)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| Vol cylinder \(= \pi \times (2x)^2 \times 9x\) \(= 36\pi x^3\) \(36\pi x^3 = \frac{4}{3}\pi r^3\) \(r^3 = 27x^3\) | \(3x\) | 3 | M1 for sub. into \(\pi r^2h\) eg. \(\pi \times (2x)^2 \times 9x\) oe M1 for \(\pi \times (2x)^2 \times 9x = \frac{4}{3}\pi r^3\) oe A1 oe eg. \(\sqrt[3]{\dfrac{36x^3}{\frac{4}{3}}}\) NB : For both method marks condone missing brackets around the \(2x\) |