Higher November 2024 Paper 1 Q12
12 A, B and C are three solid spheres.
Sphere A has a volume of 64 cm3
Sphere B has a volume of 125 cm3
The radius of sphere C is 50% of the radius of sphere B.
Work out the ratio of the surface area of sphere A to the surface area of sphere C.
Give your answer in the form \(a : b\) where \(a\) and \(b\) are integers. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 64 : 25 | P1 | for start of process to find ratio of lengths of A to B, eg \(\sqrt[3]{64}\ (= 4)\) or \(\sqrt[3]{125}\ (= 5)\) or 4 : 5 |
| P1 | for \(\sqrt[3]{125} \div 2\ (= 2.5)\) oe or \(\left(\text{``}\sqrt[3]{64}\text{''}\right)^2\ (= 16)\) | |
| P1 | for process to find ratio of areas of A to C, eg \(\text{``}4\text{''}^2 : \text{``}2.5\text{''}^2\ (= 16 : 6.25)\) | |
| A1 | for 64 : 25 oe in form \(a : b\) where \(a\) and \(b\) are integers |