Higher November 2021 Paper 2 Q19
19 \(A\), \(B\) and \(C\) are three spheres.
The volume of sphere \(A\) is 125 cm\(^3\)
The volume of sphere \(B\) is 27 cm\(^3\)
The ratio of the radius of sphere \(B\) to the radius of sphere \(C\) is \(1 : 2\)
Work out the ratio of the surface area of sphere \(A\) to the surface area of sphere \(C\). (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| 25 : 36 | P1 | for \(\sqrt[3]{125}\ (= 5)\) and \(\sqrt[3]{27}\ (= 3)\) oe OR for correct process to find the radius of A and radius of B (3.10… and 1.86…) |
| P1 | for method to find values in ratio of length between \(A\) and \(C\) eg 5 and \(2 \times 3\ (= 6)\) oe or \(\text{``}3.10\ldots\text{''}\) and \(\text{``}1.86\ldots\text{''} \times 2\ (= 3.72\ldots)\) OR 25 and 36 OR for correct process to find SA of A and SA of C (120.(8…)) and (174.(0…)) | |
| A1 | for 25 : 36 oe eg 1 : 1.44 |
Additional guidance
Accept scale factors expressed as fractions or decimals eg 1.66, 1.67, 0.6 or better
Ignore units throughout
For both P marks the lengths need not be written as a ratio