Higher June 2018 Paper 5 Q14
14 The diagram shows a cylinder and a cone.
The cylinder has radius 2 cm and height 9 cm.
The cone has radius \(r\) cm and height \(h\) cm.
The ratio \(r : h\) is 1 : 4.
The volume of the cone is equal to the volume of the cylinder.
Work out the value of \(\boldsymbol{r}\).
[The volume \(V\) of a cone with radius \(r\) and height \(h\) is \(V = \frac{1}{3}\pi r^2 h\).] [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 3 nfww | 5 | nfww - must check method before giving 5 marks must not come from wrong working | |
| B4 for \(4r^3 = 108\) or better or B3 for \(r^2 h = 108\) or M3 for \(\pi \times 2^2 \times 9 = \dfrac{1}{3}\pi r^2 4r\) oe or for \(\pi \times 2^2 \times 9 = \dfrac{1}{3}\pi \left(\dfrac{h}{4}\right)^2 h\) oe or B2 for \(36\pi\) or M1 for \(\pi \times 2^2 \times 9\) or better or B1 for \(4r\) or \(\dfrac{h}{4}\) seen | Condone use of other letter for \(r\) (or \(h\)) e.g. \(x\) For method marks allow use of 3.14, 3.142 or 22/7 for \(\pi\) | ||