Higher June 2022 Paper 1R Q20
20 The diagram shows two similar metal statues.
Diagram NOT accurately drawn
The volume of statue B is 20% less than the volume of statue A
The surface area of statue B is \(k\)% less than the surface area of statue A
Work out the value of \(k\)
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
(Length sf =) \(\sqrt[3]{0.8}\) (= 0.928…) or \(\sqrt[3]{1.25}\) (= 1.07…) or \(\sqrt[3]{4} : \sqrt[3]{5}\) oe | M1 |
(Area sf =) \(\left(\sqrt[3]{0.8}\right)^2\) (= 0.861…) or 86.1…(%) or \(\left(\sqrt[3]{1.25}\right)^2\) (= 1.16…) or 116…(%) or \(\left(\sqrt[3]{4}\right)^2 : \left(\sqrt[3]{5}\right)^2\) oe | M1 |
eg (\(k\) =) \((1 - \text{``}{0.861\ldots}\text{''}) \times 100\) or (100 – “86.1…”) or \(100 - \dfrac{100}{\text{``}{1.16}\text{''}}\) or \(100 - \dfrac{100}{\text{``}{116}\text{''}} \times 100\) or \(100 - 100 \times \dfrac{\left(\sqrt[3]{4}\right)^2}{\left(\sqrt[3]{5}\right)^2}\) | M1 |
| 13.8 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a correct linear scale factor
M1: for a correct area scale factor
M1: for a method to find the percentage reduction
A1: accept 13.7 – 13.9