4MA0 Higher June 2016 Paper 3 Q20
20 A metal cube has sides of length 4.5 cm, correct to the nearest 0.5 cm.
The cube is melted down and the metal is used to make small spheres.
Each sphere has a radius of 3 mm, correct to the nearest millimetre.
Work out the greatest number of spheres that could be made from the metal.
Show your working clearly.
(5)
| Scheme | Marks |
|---|---|
| 4.75 or 4.25 or 47.5 or 42.5 | B1 |
| 3.5 or 2.5 or 35 or 25 | B1 |
\(\dfrac{4}{3} \times \pi \times 0.25^3\) (=0.0654498…) or \(\dfrac{4}{3} \times \pi \times 2.5^3\) (=65.4498…) or 4.75 × 4.75 × 4.75 (= 107.171875) or 47.5 × 47.5 × 47.5 (=107171.875) | M1 |
| \(\text{“}4.75\text{”}^3 \div \left(\dfrac{4}{3} \times \pi \times \text{“}0.25\text{”}^3\right)\) (=1637.465...) | M1 |
| 1637 | A1 |
| (5) |
Notes
B1: Allow \(4.74\dot{9}\)
M1: Allow \(4.74\dot{9}\)
M1: indep – accept use of 4.5 and 0.3 or candidate’s bounds
units must be consistent
A1: 1637 must come from correct working with correct figures