1MA0 Higher November 2016 Paper 1 Q27
27 The diagram shows a sphere and a solid cylinder.
Diagram NOT accurately drawn
The sphere has radius 6 cm.
The solid cylinder has a base radius of 3 cm and a height of \(h\) cm.
The total surface area of the cylinder is twice the total surface area of the sphere.
Work out the ratio of the volume of the sphere to the volume of the cylinder.
Give your answer in its simplest form.
You must show all your working. (5)
| Answer | Mark | Notes |
|---|---|---|
| 32 : 45 | 5 | M1 for a correct expression for surface area of the cylinder (\(=2 \times \pi \times 3^2 + 6\pi h\)) or surface area of the sphere (\(=4 \times \pi \times 6^2\)) M1 (dep) for equating ‘surface area of cylinder’ and ‘2 \(\times\) surface area of sphere’, \(2 \times \pi \times 3^2 + 6\pi h = 2 \times 4 \times \pi \times 6^2\) M1 (dep) for a method to isolate \(h\) M1 for \(\pi \times 3^2 \times \text{‘}45\text{’}\) oe and \(\dfrac{4}{3} \times \pi \times 6^3\) oe A1 cao |