Higher June 2019 Paper 6 Q18
18 A cone has radius \(r\) cm and height \(h\) cm.
The height is three times the radius.
The volume of the cone is 2100 cm\(^3\).
Calculate the radius of the cone.
[The volume \(V\) of a cone with radius \(r\) and height \(h\) is \(V = \frac{1}{3}\pi r^2 h\).] [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 8.74[…] nfww | 4 | M3 for [\(r =\)] \(\sqrt[3]{\dfrac{2100}{\pi}}\) or M2 for \(\pi r^3 = 2100\) oe M1 for \(\frac{1}{3}\pi r^2(3r)\) oe Alternative method using \(h\) M3 for [\(h =\)] \(\sqrt[3]{\dfrac{56700}{\pi}}\) soi by 26.2[3…] or M2 for \(\pi h^3 = 56700\) oe M1 for \(\frac{1}{3}\pi\left(\frac{h}{3}\right)^2 h\) oe | Accept answer of 8.7 after M3 May be done in stages e.g. M3 for \(\sqrt[3]{668.(\ldots)}\) e.g. M2 for \(3\pi r^3 = 6300\) or \(\frac{1}{3}\pi r^2(3r) = 2100\) etc e.g. M1 for \(\pi r^3\) e.g. M1 for \(\frac{1}{27}\pi h^3\) |