Higher November 2021 Unit 1 Q11
11. Two similar solids are shown below.
Diagrams not drawn to scale
Solid A has a height of 5 cm.
Solid B has a height of 7 cm.
Mari claims that the surface area of solid B is more than double the surface area of solid A.
Is Mari correct?
You must justify your answer. [2]
| Scheme | Marks | Comments |
|---|---|---|
| (Area scale factor =) Sight of \(\left(\tfrac{7}{5}\right)^2\ \left(= \tfrac{49}{25}\right)\) OR \(1{\cdot}4^2\ (= 1{\cdot}96)\) | B1 | Or equivalent Accept a method based on ratios e.g. \(5^2 : 7^2 = 25 : 49 = 1 : \tfrac{49}{25}\) |
| \(\tfrac{49}{25}\ (< 2)\) or \(1{\cdot}96\ (< 2)\) AND ‘No (Mari is not correct)’ | B1 | Accept any equivalent statement. Accept \(\left(\tfrac{7}{5}\right)^2 < 2\) or \(1{\cdot}4^2 < 2\) or equivalent. B0 if evaluation of \(\left(\tfrac{7}{5}\right)^2\) or \(1{\cdot}4^2\) is incorrect. |
Alternative method (using scale factor 2)
| Scheme | Marks | Comments |
|---|---|---|
| \(5^2 \times 2\ (= 50)\) | B1 | Accept a method based on ratios e.g. \(5^2 : 7^2 = 25 : 49 = \tfrac{25}{49} : 1\) |
| \((7^2 =)\ 49 < 50\) AND ‘No (Mari is not correct)’ | B1 | Accept any equivalent statement e.g. \(\sqrt{49}<\sqrt{50}\) B0 if evaluation of \(5^2\) or \(7^2\) is incorrect. |