4MA0 Higher January 2017 Paper 4R Q19
19 The diagram shows a solid cone.
Diagram NOT accurately drawn
The radius of the base of the cone is 5 cm.
The total surface area of the cone is \(90\pi\) cm\(^2\)
Work out the volume of the cone.
Give your answer as a multiple of \(\pi\).
(5)
| Scheme | Marks |
|---|---|
| \((\pi \times 5^2) + \pi \times 5 \times l\) \((25\pi) + 5\pi l\) | M1 |
| (\(l =\)) 13 | A1 |
| (\(h =\)) \(\sqrt{13^2 - 5^2}\) or \(\sqrt{144}\) or 12 | M1 |
| (\(V =\)) \(\dfrac{1}{3} \times \pi \times 5^2 \times 12\) (= 314 – 314.3) | M1 |
| \(100\pi\) | A1 |
| (5) | |
| (5 marks) |
Notes
M1: For a correct expression for total surface area
A1: For the correct slant height
M1: For the correct method to find \(h\)
ft if first M1 scored
M1: For the correct method to find \(V\)
ft if first M1 scored