Higher November 2021 Paper 3 Q26
26 Here are two similar cones.
The surface area of cone A is 2 m2
The surface area of cone B is 4.5 m2
Work out the ratio \(\qquad\) radius of cone A : radius of cone B
Give your answer in the form \(\quad 1 : n\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(4.5 \div 2\) or 2.25 | M1 | |
| \(\sqrt{\text{their } 2.25}\) or 1.5 | M1dep | |
| 1 : 1.5 or \(1 : 1\dfrac{1}{2}\) or \(1 : \dfrac{3}{2}\) | A1 | |
| Alternative method 2 | ||
| \(\sqrt{2} : \sqrt{4.5}\) | M1 | |
| \(1 : \dfrac{\sqrt{\text{their } 4.5}}{\sqrt{\text{their } 2}}\) | M1dep | |
| 1 : 1.5 or \(1 : 1\dfrac{1}{2}\) or \(1 : \dfrac{3}{2}\) | A1 | |
| Alternative method 3 | ||
| \(\sqrt{4} : \sqrt{9}\) | M1 | |
| 2 : 3 | M1dep | |
| 1 : 1.5 or \(1 : 1\dfrac{1}{2}\) or \(1 : \dfrac{3}{2}\) | A1 | |
| Alternative method 4 | ||
| \(2 \div 4.5\) or \(\dfrac{4}{9}\) or \(0.\dot{4}\) | M1 | accept 0.44 or better |
| \(\sqrt{\text{their } \dfrac{4}{9}}\) or \(\dfrac{2}{3}\) or \(0.\dot{6}\) and \(\dfrac{2}{3} : 1\) | M1dep | accept 0.66 or better |
| 1 : 1.5 or \(1 : 1\dfrac{1}{2}\) or \(1 : \dfrac{3}{2}\) | A1 | |
Additional guidance
| 1 : 1.5 on answer line with no evidence of incorrect method | M1M1A1 |