Higher June 2024 Paper 2 Q17
17 L, M and P are three similar solid cylinders made from the same material.
L has a mass of 64 g
M has a mass of 125 g
M has a total surface area of 144 cm2
P has a total surface area of 16 cm2
Work out
height of cylinder L : height of cylinder M : height of cylinder P (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 12 : 15 : 5 | P1 | for process to find ratio of heights of L and M eg \(\sqrt[3]{64} : \sqrt[3]{125}\ (= 4 : 5)\) oe or \(\sqrt[3]{\dfrac{64}{64}} : \sqrt[3]{\dfrac{125}{64}}\ (= 1 : 1.25)\) oe or \(\sqrt[3]{\dfrac{64}{125}} : \sqrt[3]{\dfrac{125}{125}}\ (= 0.8 : 1)\) oe |
| P1 | for process to find ratio of heights of M and P eg \(\sqrt{144} : \sqrt{16}\ (= 12 : 4 = 3 : 1)\) oe or \(\sqrt{\dfrac{144}{16}} : \sqrt{\dfrac{16}{16}}\ (= 3 : 1)\) oe or \(\sqrt{\dfrac{144}{144}} : \sqrt{\dfrac{16}{144}}\ (= 1 : 0.\dot{3})\) oe | |
| P1 | (dep on P2) for process to find ratio of heights of all 3, eg \(\text{``}(4 : 5)\text{''} \times 3\) and \(\text{``}(3 : 1)\text{''} \times 5\) or \((1 : 1.25) \times 12\) and \((3 : 1) \times 5\) or \((0.8 : 1)\) and \((1 : 0.\dot{3})\) | |
| A1 | for 12 : 15 : 5 oe |
Additional guidance
Condone not written as a ratio as long as clear
\(\dfrac{125}{64} = 1.953\ldots\) \(\dfrac{64}{125} = 0.512\)
Condone not written as a ratio as long as clear
\(\dfrac{144}{16} = 9\) \(\dfrac{16}{144} = 0.\dot{1}\)
Can ISW incorrect simplification of a correct ratio