Higher June 2022 Unit 2 Q17
17. Solid A and Solid B are similar.
Solid A has a volume of 8000 cm3 and a height of 30 cm.
Solid B has a volume of 4913 cm3.
Calculate the height of Solid B. [3]
Height of Solid B = …………… cm
Method using the linear scale factor
| Scheme | Marks | Comments |
|---|---|---|
| (Linear scale factor=) \(\sqrt[3]{\dfrac{4913}{8000}}\) OR \(\dfrac{\sqrt[3]{4913}}{\sqrt[3]{8000}}\) (= 0·85 or \(\frac{17}{20}\)) | B1 | Or equivalent. |
| (Height of Solid B=) \(\sqrt[3]{\dfrac{4913}{8000}} \times 30\) | M1 | F.T. their derived linear scale factor (from \(\sqrt[3]{\ }\)) |
| = 25·5 (cm) | A1 | CAO. |
17. Alternative method using the linear scale factor
| Scheme | Marks | Comments |
|---|---|---|
| (Linear scale factor=) \(\sqrt[3]{\dfrac{8000}{4913}}\) OR \(\dfrac{\sqrt[3]{8000}}{\sqrt[3]{4913}}\) (=1·17647… or \(\frac{20}{17}\) ) | B1 | Or equivalent. |
| (Height of Solid B=) 30 ÷ \(\sqrt[3]{\dfrac{8000}{4913}}\) | M1 | F.T. their derived linear scale factor (from \(\sqrt[3]{\ }\)) |
| = 25·5(cm) | A1 | CAO |
17. Method using the volume scale factor
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{h^3}{30^3} = \dfrac{4913}{8000}\) (=0·614…) | B1 | Must include \(\dfrac{h^3}{30^3}\) or equivalent, e.g. \(\left(\dfrac{h}{30}\right)^3 = \dfrac{4913}{8000}\) |
| (Height of solid B=) \(\sqrt[3]{30^3 \times \dfrac{4913}{8000}}\) OR \(\sqrt[3]{30^3 \div \dfrac{8000}{4913}}\) | M1 | |
| = 25·5 (cm) | A1 | CAO |
17. Alternative method using the volume scale factor
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{30^3}{h^3} = \dfrac{8000}{4913}\) (=1·628…) | B1 | Must include \(\dfrac{30^3}{h^3}\) or equivalent, e.g. \(\left(\dfrac{30}{h}\right)^3 = \dfrac{8000}{4913}\) |
| (Height of solid B=) \(\sqrt[3]{30^3 \div \dfrac{8000}{4913}}\) OR \(\sqrt[3]{30^3 \times \dfrac{4913}{8000}}\) | M1 | |
| = 25·5 (cm) | A1 | CAO |