Higher June 2019 Paper 2 Q21
21 A solid shape is made by joining two cones.
Each cone has the same radius.
One cone has \(\quad\) slant height \(= 2 \times\) radius
The other cone has \(\quad\) slant height \(= 3 \times\) radius
The total surface area of the shape is \(\quad 57.8\pi\) cm2
Work out the radius. [3 marks]
| Curved surface area of a cone \(= \pi r l\) \(\quad\) where \(r\) is the radius and \(l\) is the slant height |
| Answer | Mark | Comments |
|---|---|---|
| \(\pi r \times 2r\) or \(\pi r \times 3r\) or \(2\pi r^2\) or \(3\pi r^2\) or \(5\pi r^2\) | M1 | oe implied by a correct equation for first A1 |
| \(2\pi r^2 + 3\pi r^2 = 57.8\pi\) or \(5\pi r^2 = 57.8\pi\) or \(2\pi r^2 = 57.8\pi \div 5 \times 2\) or \(3\pi r^2 = 57.8\pi \div 5 \times 3\) or \(\sqrt{11.56}\) | A1 | oe eg \(\pi r \times 2r + \pi r \times 3r = 57.8\pi\) or \(5r^2 = 57.8\) or \(r^2 = 11.56\) or \(2r^2 = 23.12\) or \(3r^2 = 34.68\) |
| 3.4 or \(\dfrac{17}{5}\) or \(3\dfrac{2}{5}\) | A1 |
Additional guidance
| 11.56 not in a square root or a correct equation | M0 |
| Adding the area of a circle (or 2 circles) can score a maximum of M1A0A0 eg \(3\pi r^2 + \pi r^2 = 57.8\pi\) Adding further incorrect terms scores M0 | M1A0A0 |
| T & I scores M1A1A1 if answer 3.4, otherwise scores 0 | |
| Allow \(\pi r^2 5\) for \(5\pi r^2\) etc throughout | |
| Answer \(\pm\) 3.4 | M1A1A0 |
| \(5\pi r^2 \times \pi r^2\) or \(3\pi r^2 \times \pi r l\) etc | M0 |
| Allow \(\pi\) to be replaced by [3.14, 3.142] | |
| Answer 3 is incorrect unless 3.4 seen in working lines |