Higher January 2023 Paper 2 Q19
19 A and B are two similar vases.
Diagram NOT accurately drawn
The vases are such that
surface area of vase B \(= \dfrac{25}{64} \times\) surface area of vase A
and that
volume of vase A – volume of vase B = 541.8 cm3
Calculate the volume of vase B
(4)
| Scheme | Marks |
|---|---|
eg \(\sqrt{\dfrac{25}{64}}\left(= \dfrac{5}{8} = 0.625\right)\) or \(\sqrt{\dfrac{64}{25}}\left(= \dfrac{8}{5} = 1.6\right)\) or \(\sqrt{25} : \sqrt{64}\;(5:8)\) or \(\sqrt{64} : \sqrt{25}\;(8:5)\) or \(\dfrac{(\sqrt{25})^3}{(\sqrt{64})^3} = \left(\dfrac{125}{512} = 0.244140625\right)\) oe or \(\dfrac{512}{125} = 4.096\) \(\dfrac{25^3}{64^3} = \dfrac{(\text{vol of }\mathbf{B})^2}{(\text{vol of }\mathbf{B} + 541.8)^2}\) or \(\dfrac{25}{64} = \dfrac{(\text{vol of }\mathbf{B})^{\frac{2}{3}}}{(\text{vol of }\mathbf{B} + 541.8)^{\frac{2}{3}}}\) oe | M1 |
eg \(\mathbf{B}\left(\dfrac{512}{125} - 1\right) = 541.8\) or \(3.096\mathbf{B} = 541.8\) oe or eg \(\mathbf{A}\left(1 - \dfrac{125}{512}\right) = 541.8\) or \(\dfrac{387}{512}\mathbf{A} = 541.8\) \((8^3)k - (5^3)k\;(= 387k) = 541.8\) or eg \((k =)\;\dfrac{541.8}{387}\left(= \dfrac{7}{5}\right)\) | M1 |
eg \((\mathbf{B})\;541.8 \div \text{``}{\dfrac{387}{125}}\text{''}\) or \(541.8 \div \text{``}{3.096}\text{''}\) or eg \(125 \times \text{``}{\dfrac{7}{5}}\text{''}\) or \((\mathbf{A})\;541.8 \div \text{``}{\dfrac{387}{512}}\text{''}\;(= 716.8)\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 175 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a correct scale factor for length – may be given as a fraction or decimal or ratio
or
a correct scale factor for volume given as a fraction or decimal or ratio
or
a correct equation for the volume of vase B
M1: For a correct equation for the volume of B or a correct equation for the volume of A
M1: For a completely correct method to find the volume of vase B or vase A
A1: cao