Higher November 2024 Unit 2 Q8
8. The diagram shows a solid cylinder with radius 10 cm.
The total surface area of the solid cylinder is 1570·8 cm2.
Diagram not drawn to scale
Find the height of the cylinder. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (Area of top or bottom =) \(\pi \times 10^2\) (× 2) | M1 | May be seen or implied in later working. Award M1 for sight of an appropriate answer between either:
|
| (Curved surface area =) \(2 \times \pi \times 10 \times\) height or equivalent (e.g.62·8(31...) × h) | M1 | May be seen or implied in later working. |
| (Height =) \(\dfrac{1570{\cdot}8 - \pi \times 10^2 \times 2}{2 \times \pi \times 10}\) \(\left(= \dfrac{942{\cdot}48}{62{\cdot}83}\right)\) or \(\dfrac{1570{\cdot}8}{2 \times \pi \times 10} - 10\) or equivalent | M2 | Award M2 for isolating the height term. FT for M2 or M1 for ‘their \(\pi \times 10^2\)’ × 2 and ‘their \(\pi \times 20\)’, provided that:
Award M1 for equating the three areas to 1570·8 but not isolating the height term e.g.
|
| Answer between 14·99 and 15·02 (cm) inclusive | A1 | CAO. |