Higher June 2021 Paper 2 Q20
20 Mathematically similar wooden blocks are made in a workshop.
There are small blocks and there are large blocks.
The volume of each small block is 300 cm3
Given that
the surface area of each small block : the surface area of each large block = 25 : 36
work out the volume of each large block.
(3)
| Scheme | Marks |
|---|---|
eg \(\sqrt{\dfrac{36}{25}}\ \left(= \dfrac{6}{5}\right)\) or \(\sqrt{\dfrac{25}{36}}\ \left(= \dfrac{5}{6}\right)\) or \(\sqrt{36} : \sqrt{25}\ (6 : 5)\) or \(\sqrt{25} : \sqrt{36}\ (5 : 6)\) or \(\dfrac{(\sqrt{25})^3}{(\sqrt{36})^3} = \left(\dfrac{125}{216}\right)\) oe or \(\dfrac{36^3}{25^3} = \dfrac{(\text{vol of large})^2}{300^2}\) or \(\dfrac{36}{25} = \dfrac{(\text{vol of large})^{\frac{2}{3}}}{300^{\frac{2}{3}}}\) oe | M1 |
eg \(300 \times \left(\text{``}\dfrac{6}{5}\text{''}\right)^3\) or \(300 \div \left(\text{``}\dfrac{5}{6}\text{''}\right)^3\) oe or \(\sqrt{\dfrac{300^2 \times 36^3}{25^3}}\) or \(\left(\dfrac{36 \times 300^{\frac{2}{3}}}{25}\right)^{\frac{3}{2}}\) oe | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: 518.4 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for a correct scale factor for length – may be given as a fraction or ratio
or
a correct scale factor for volume given as a fraction or ratio
or
a correct equation for the volume of each large block
M1: for a complete method to find the volume of a large block
A1: allow 518