Higher November 2021 Paper 3 Q13
13 A box is the shape of half a cylinder on top of a cuboid.
Work out the volume of the box. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(4 \times 26 \times 15\) or 1560 | M1 | |
| \(\pi \times (26 \div 2)^2 \times 15\ (\div 2)\) or \(\pi \times 13^2 \times 15\ (\div 2)\) or \(2535\pi\ (\div 2)\) or \(\pi \times (26 \div 2)^2 \div 2\ (\times 15)\) or \(\pi \times 13^2 \div 2\ (\times 15)\) or \(\dfrac{169\pi}{2}\ (\times 15)\) or \(84.5\pi\ (\times 15)\) or \([265.3, 265.5]\ (\times 15)\) or \([7959.9, 7965]\ (\div 2)\) | M1 | oe accept [3.14, 3.142] for \(\pi\) |
| \(\dfrac{2535\pi}{2}\) or \(1267.5\pi\) or [3979.95, 3982.5] | M1dep | dep on previous mark |
| [5539, 5543] | A1 | |
| Alternative method 2 | ||
| \(4 \times 26\) or 104 | M1 | |
| \(\pi \times (26 \div 2)^2 \div 2\) or \(\pi \times 13^2 \div 2\) or \(\dfrac{169\pi}{2}\) or [265.3, 265.5] | M1 | accept [3.14, 3.142] for \(\pi\) |
| (their \(104 +\) their \(\dfrac{169\pi}{2}) \times 15\) or \([369.3, 369.5] \times 15\) | M1dep | dep on M1M1 |
| [5539, 5543] | A1 | |