4MA0 Higher June 2016 Paper 4 Q20
20
Diagram NOT accurately drawn
The diagram shows a solid shape made from a cone on top of a cylinder.
The cone has a radius of 10 cm and a height of 10 cm.
The cylinder has a radius of 10 cm and a height of 10 cm.
The centre of the base of the cone coincides with the centre of the top face of the cylinder.
The total surface area of the solid is \(A\) cm²
Show that \(A = (300 + 100\sqrt{2})\pi\)
(4)
| Scheme | Marks |
|---|---|
| \(\pi \times 20 \times 10\) or \(200\pi\) or 628.(318…) oe | M1 |
| \(\sqrt{10^2 + 10^2}\) or \(10\sqrt{2}\) or 14.1(421…) oe | M1 |
\(\pi \times 10 \times 10\sqrt{2}\) or \(100\pi\sqrt{2}\) or 444.(288…) or 141.(421…)\(\pi\) oe | M1dep |
Eg \(100\pi + 200\pi + \pi \times 10 \times 10\sqrt{2}\) Answer: Correct solution | A1 |
| (4) |
Notes
M1: For the curved surface area of the cylinder
M1: For the slant height of the cone
M1dep: For the curved surface area of the cone
A1: cso
For a correct exact expression for the total surface area that will lead to \((300 + 100\sqrt{2})\pi\)
Dep on M3