4MA0 Higher January 2017 Paper 3 Q16
16 The diagram shows two mathematically similar pots, A and B.
Diagram NOT accurately drawn
A has a volume of 264 cm\(^3\)
B has a volume of 891 cm\(^3\)
A has a height of 8 cm
(a) Work out the height of pot B. (2)
B has a surface area of 459 cm\(^2\)
(b) Work out the surface area of pot A. (2)
| Scheme | Marks |
|---|---|
\(\sqrt[3]{\dfrac{264}{891}}\) or \(\sqrt[3]{\dfrac{891}{264}}\) or \(\dfrac{2}{3}\) or or \(\dfrac{3}{2}\) oe or 2 : 3 or \(\sqrt[3]{264} : \sqrt[3]{891}\) (= 6.415:9.622) | M1 |
| 12 | A1 |
| (2) |
Notes
M1: correct linear scale factor
or correct ratio
(numbers may be in either order)
A1: cao
| Scheme | Marks |
|---|---|
\(459 \times \left(\dfrac{2}{3}\right)^2\) oe or \(459 \div \left(\dfrac{3}{2}\right)^2\) oe or 459 × 41(.153…) ÷ 92(.594…) | M1 |
| 204 | A1 |
| (2) | |
| (4 marks) |
Notes
M1: correct method to find the surface area of A
A1: cao