Higher November 2020 Unit 1 Q13
13. Two similar cones have volumes of 20 cm3 and 1280 cm3.
The radius of the base of the smaller cone is 2·3 cm.
Calculate the radius of the base of the larger cone. [3]
| Scheme | Marks | Comments |
|---|---|---|
| (Linear scale factor =) \(\sqrt[3]{(1280 / 20)}\) (= 4) | B1 | Or equivalent. Accept a method based on ratios e.g. 1 : 4 (from 20 : 1280 = 1 : 64 = 1 : 43) |
| \(\sqrt[3]{(1280 / 20)} \times 2{\cdot}3\) | M1 | FT their derived scale factor (from \(\sqrt[3]{\phantom{x}}\)). |
| = 9·2 (cm) | A1 | SC1 for an answer of 18.4 (using s.f. of 8, from \(\sqrt{64}\)). |
Alternative method (using reciprocal scale factor)
| Scheme | Marks | Comments |
|---|---|---|
| (Linear scale factor =) \(\sqrt[3]{(20 / 1280)}\) (= 1 / 4) | B1 | Or equivalent. Accept a method based on ratios. |
| \(2{\cdot}3 \div \sqrt[3]{(20 / 1280)}\) OR \(1 / \sqrt[3]{(20 / 1280)} \times 2{\cdot}3\) | M1 | FT their derived scale factor (from \(\sqrt[3]{\phantom{x}}\)). |
| = 9·2 (cm) | A1 |