Higher January 2023 Paper 2R Q18
18 A statue and a model of the statue are mathematically similar.
The statue has a total surface area of 3600 cm2
The model has a total surface area of 625 cm2
The volume of the model is 750 cm3
Work out the volume of the statue.
(3)
| Scheme | Marks |
|---|---|
\(\sqrt{\dfrac{3600}{625}}\) or \(\dfrac{12}{5}\) oe or 2.4 or 12:5 oe or \(\sqrt{\dfrac{625}{3600}}\) or \(\dfrac{5}{12}\) oe or 0.416.... or 5:12 oe or \(\dfrac{3600^3}{625^3} = \dfrac{(\text{vol of statue})^2}{750^2}\) oe or \(\dfrac{3600}{625} = \dfrac{(\text{vol of statue})^{\frac{2}{3}}}{750^{\frac{2}{3}}}\) oe | M1 |
eg \(750 \times \left(\text{``}{\dfrac{12}{5}}\text{''}\right)^3\) oe or \(750 \div \left(\text{``}{\dfrac{5}{12}}\text{''}\right)^3\) oe or \(\sqrt{\dfrac{3600^3 \times 750^2}{625^3}}\) oe or \(\left(\dfrac{3600 \times 750^{\frac{2}{3}}}{625}\right)^{\frac{3}{2}}\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 10 368 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for a correct length scale factor or a correct length ratio or setting up a correct equation involving the volume of the statue
M1: (dep on M1) for a correct method to work out the volume of the statue
A1: cao