Higher November 2020 Paper 6 Q14
14 The base of a cone is fixed to the top of a cylinder to make a decoration.
The radius of the base of the cone and of the cylinder is \(r\) cm.
The cone’s height is \(5r\) cm.
The total height of the decoration is \(6r\) cm.
The total volume of the decoration is 225 cm3.
Calculate the value of \(r\).
Show your working.
[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 | |
|---|---|---|---|
| 2.99 [cm] with correct working | 5 | M3 for \(\frac{5}{3}\pi r^3 + \pi r^3 = 225\) soi by \(\frac{8}{3}\pi r^3 = 225\) A1 for \(\sqrt[3]{\frac{675}{8\pi}}\) or \(\sqrt[3]{26.8}\) to \(\sqrt[3]{26.9}\) or M2 for \(\frac{1}{3}\pi r^2 \times 5r + \pi r^2 \times r\) oe soi by \(\frac{8}{3}\pi r^3\) or M1 for \(\frac{1}{3}\pi r^2 \times 5r\) oe or \(\pi r^2 \times r\) oe If 0 or M1 scored, instead award SC2 for answer 2.99 or greater rot accuracy of 2.9947090608… with no working or insufficient working If 0 scored SC1 for \(\sqrt[3]{\frac{675}{8\pi}}\) or \(\sqrt[3]{26.8}\) to \(\sqrt[3]{26.9}\) with no working | “Correct working” requires evidence of at least M2 Accept 2.99 or greater rot accuracy of 2.9947090608 with correct working Accept 3[.0] as final answer only after M3A1 Trials: Full marks for trials leading to an answer 2.99 or greater rot accuracy of 2.9947090608… Trials leading to any other final answer, including 3[.0], only score the M marks if seen |