Higher November 2016 Unit 1 Q10
10. The radius of a hemisphere and the radius of a cylinder are equal.
The hemisphere and cylinder have equal volumes.
Calculate the ratio of the height of the cylinder to the radius of the cylinder. [3]
height of cylinder : radius of cylinder
= ………………… : …………………
From the formula list: Volume of sphere \(= \dfrac{4}{3}\pi r^3\)
| Scheme | Marks | Comments |
|---|---|---|
| \(\tfrac{2}{3}\pi r^3 = \pi r^2 h\) or equivalent | M1 | |
| \(\dfrac{2r}{3} = h\) or equivalent. | A1 | Must be in terms of \(r\), \(h\). Allow inclusion of π, e.g. 2πr = 3πh. |
| (Height cyl. : Radius cyl. = ) 2 : 3 or equivalent. | A1 | If no other marks awarded allow SC1 for 3 : 2 If working with a whole sphere, award SC2 for 4 : 3 OR SC1 for 4r/3 = h |