Higher June 2017 Paper 1 Q28
28 Volume of cone \(= \dfrac{1}{3}\pi r^2 h\) \(\;\) where \(r\) is the radius and \(h\) is the perpendicular height.
A cone has a
- horizontal base of radius 5 cm
- height of 15 cm
The cone contains water to a depth of 9 cm
Work out the volume of the water, in cm\(^3\)
Give your answer in terms of \(\pi\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{1}{3}\ (\times)\ \pi\ (\times)\ 5^2\ (\times)\ 15\) or \(125\pi\) or [392.5, 392.8] | M1 | oe |
| \(\dfrac{r}{5} = \dfrac{15 - 9}{15}\) or \(r = 2\) | M1 | oe \(r\) is radius of small cone |
| \(\dfrac{1}{3} \times \pi \times\) their \(2^2 \times (15 - 9)\) or \(8\pi\) or [25.12, 25.14] | M1dep | dep on 2nd M1 |
| \(117\pi\) | A1 | Accept \(\pi 117\) or \(\dfrac{351\pi}{3}\) |
| Alternative method 2 | ||
| \(\dfrac{1}{3}\ (\times)\ \pi\ (\times)\ 5^2\ (\times)\ 15\) or \(125\pi\) or [392.5, 392.8] | M1 | oe |
| volume sf \(= \left(\dfrac{15 - 9}{15}\right)^3\) or \(\dfrac{8}{125}\) or \(\left(\dfrac{15}{15 - 9}\right)^3\) or \(\dfrac{125}{8}\) | M1 | oe |
| their \(125\pi \times\) their \(\dfrac{8}{125}\) or their \(125\pi \div\) their \(\dfrac{125}{8}\) or \(8\pi\) or [25.12, 25.14] | M1dep | dep on 2nd M1 Accept \(1 - \dfrac{8}{125}\) or \(\dfrac{117}{125}\) |
| \(117\pi\) | A1 | Accept \(\pi 117\) or \(\dfrac{351\pi}{3}\) |
Additional guidance
| Allow [3.14, 3.142] for \(\pi\) for M marks only | |
| Answer of \(367.(\ldots)\) | M1M1M1A0 |