Higher June 2018 Paper 2 Q23
23 Solids X and Y are similar.
X has volume 64 cm\(^3\)
Y has volume 343 cm\(^3\)
The surface area of X is 176 cm\(^2\)
Work out the surface area of Y. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\sqrt[3]{64}\) and \(\sqrt[3]{343}\) or 4 and 7 or \(\sqrt[3]{[5.3, 5.4]}\) or [1.74, 1.754411] or \(\sqrt[3]{[0.18, 0.19]}\) or [0.56, 0.575] | M1 | oe eg 4 : 7 or 7 : 4 or \(\sqrt[3]{\dfrac{343}{64}}\) or \(\dfrac{7}{4}\) or \(\sqrt[3]{\dfrac{64}{343}}\) or \(\dfrac{4}{7}\) |
| their \(4^2\) and their \(7^2\) or 16 and 49 or their \([1.74, 1.754411]^2\) or [3.02, 3.08] or their \([0.56, 0.575]^2\) or [0.31, 0.331] | M1dep | oe eg 16 : 49 or 49 : 16 or \(\left(\text{their } \dfrac{7}{4}\right)^2\) or \(\dfrac{49}{16}\) or \(\left(\text{their } \dfrac{4}{7}\right)^2\) or \(\dfrac{16}{49}\) |
| 539 | A1 |
Additional guidance
| \(4^3\) and \(7^3\) | M1 |
| \(64^{\frac{2}{3}}\) and \(343^{\frac{2}{3}}\) | M1M1 |
| \(\left(\dfrac{343}{64}\right)^{\frac{2}{3}}\) or \(\left(\dfrac{64}{343}\right)^{\frac{2}{3}}\) | M1M1 |
| Answer 539 with evidence of rounding to 539 scores A0 | |
| eg1 \(176 \times 3.06 = 538.56\) Answer 539 | M1M1A0 |
| eg2 \(176 \times 3.06 = 539\) (may have kept all digits on calculator) | M1M1A1 |
| \(\left(\sqrt{176} \times \dfrac{7}{4}\right)^2\) | M1M1 |
| \(176 \div 16 = 11\) and \(11 \times 49\) | M1M1 |
| 4 and 7 (and/or \(4^2\) and \(7^2\)) but uses different method not involving 4 and 7 | M1M0A0 |