Higher January 2022 Paper 1R Q18
18 The three solids A, B and C are similar such that
the surface area of A : the surface area of B = 4 : 9
and
the volume of B : the volume of C = 125 : 343
Work out the ratio
the height of A : the height of C
Give your ratio in its simplest form.
(4)
| Scheme | Marks |
|---|---|
\(\sqrt{4} : \sqrt{9}\ (= 2 : 3)\) or \(\dfrac{\sqrt{4}}{\sqrt{9}}\left(= \dfrac{2}{3}\right)\) oe or \(\sqrt{9} : \sqrt{4}\ (= 3 : 2)\) or \(\dfrac{\sqrt{9}}{\sqrt{4}}\left(= \dfrac{3}{2}\right)\) oe | M1 |
\(\sqrt[3]{125} : \sqrt[3]{343}\ (= 5 : 7)\) or \(\dfrac{\sqrt[3]{125}}{\sqrt[3]{343}}\left(= \dfrac{5}{7}\right)\) oe or \(\sqrt[3]{343} : \sqrt[3]{125}\ (= 7 : 5)\) or \(\dfrac{\sqrt[3]{343}}{\sqrt[3]{125}}\left(= \dfrac{7}{5}\right)\) oe | M1 |
| \(A : B = 10 : 15\) and \(B : C = 15 : 21\) oe | M1 |
| 10 : 21 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for finding the ratio or fraction for lengths for \(A : B\) or \(B : A\)
M1: for finding the ratio or fraction for lengths for \(B : C\) or \(C : B\)
M1: for manipulating \(A : B\) and \(B : C\) so that both \(B\) values are equal
A1: Allow 1 : 2.1
SC3 for 21 : 10 with all working shown