18 Percy sells paint in standard tins and large tins. The standard tin covers 40 m\(^2\) and the large tin covers 60 m\(^2\).
(a) Percy publishes this chart showing the area that can be covered with each tin of paint.
Explain why the chart is misleading. [1]
(b) The standard tin and the large tin are mathematically similar. The volume of the large tin is 50% more than the volume of the standard tin. Both tins are cylinders. The radius of the standard tin is 10 cm.
Calculate the radius of the large tin. [4]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Bars are of different width oe
1
0 for large tin looks larger than it is 0 for the bars are different sizes 0 for incorrect/no \(x\)-axis
Mark scheme (b)
Answer
Marks
Part marks and guidance
11.4[...] nfww
4
B1 for 1.5 or \(\dfrac{3}{2}\) or 3 : 2 soi
AND
M2 for \(10 \times \sqrt[3]{1.5}\)
or
M1 for \(\sqrt[3]{1.5}\) soi by 1.14(47…)
If 0 scored allow SC1 for 15 as final answer or seen radius of large tin
Alternative: B1 for 0.666 to 0.667 or \(\dfrac{2}{3}\) or 2 : 3 soi AND
M2 for \(10 \div \sqrt[3]{0.666 \text{ to } 0.667}\) oe
or
M1 for \(\sqrt[3]{0.666 \text{ to } 0.667}\) oe soi 0.873(…)
