Higher January 2019 Paper 1R Q17
17 Here are a solid sphere and a solid cylinder.
Diagram NOT accurately drawn
The radius of the sphere is \(r\) cm.
The radius of the cylinder is \(r\) cm.
The height of the cylinder is \(2r\) cm.
The total surface area of the cylinder is \(k\pi\) cm²
(a) Find an expression for \(k\) in terms of \(r\). (2)
(b) Show that the ratio
total surface area of the cylinder : total surface area of the sphere
is the same as the ratiovolume of the cylinder : volume of the sphere
(3)| Scheme | Marks |
|---|---|
| \(2\pi r^2 + 2\pi r \times 2r\) | M1 |
| \(6r^2\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| S.A. \(6\pi r^2 : 4\pi r^2 = 3 : 2\) | M1 |
| \(\mathrm{V_c} : \mathrm{V_s} = 2\pi r^3 : \dfrac{4}{3}\pi r^3\) | M1 |
| \(= 3 \times 2 : 4 = 3 : 2\) Answer: Shown | A1 |
| (3) | |
| (5 marks) |
Notes
M1: ft their answer from (a), must be in terms of \(r\).
Ratios could be seen as fractions throughout eg \(\dfrac{3}{2}\)
A1: oe eg ratios could be \(\dfrac{3}{2} : 1\)