Higher June 2022 Unit 2 Q3
3. The height of a cylinder is 24·8 cm.
The ratio of the diameter of the cylinder to the height of the cylinder is 3 : 2.
Find the volume of the cylinder.
Give your answer correct to 2 significant figures.
You must show all your working. [5]
| Scheme | Marks | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| (Diameter =) 24·8 ÷ 2 × 3 OR (Radius =) 24·8 ÷ 2 × 3 ÷ 2 or equivalent | M1 | |||||||||
| (Diameter =) 37·2 (cm) OR (Radius =) 18·6 (cm) | A1 | Sight of 1086 to 1087 (cm2) (base area calculated with radius 18·6 ) OR 4345 to 4348 (cm2) (base area calculated with diameter) implies first M1 A1. If diameter AND radius given and radius ≠ 18·6 either:
| ||||||||
| \(\pi \times \left(\frac{37.2}{2}\right)^2 \times 24{\cdot}8\) or \(\pi \times 18{\cdot}6^2 \times 24{\cdot}8\) | M1 | May be seen in parts. Accept 3·14 × 18·62 × 24·8 or equivalent. FT ‘their stated radius’ OR ‘their stated diameter’, provided it is halved at the appropriate stage. | ||||||||
| = 27 000 (cm3) | A2 | For A2, must be correct to 2sf. A1 for an answer between 26 940 and 26 960 (cm3) inclusive. Note:
If M0 (2nd M mark) then award SC1 for an answer of either:
|