4400 Higher June 2006 Paper 3 Q22
22 A cylindrical tank has a radius of 30 cm and a height of 45 cm.
The tank contains water to a depth of 36 cm.
A metal sphere is dropped into the water and is completely covered.
The water level rises by 5 cm.
Diagram NOT accurately drawn
Calculate the radius of the sphere.
(5)
| Scheme | Marks |
|---|---|
| \(\pi \times 30^2 \times 5\) or \(\pi \times 30^2 \times 41 - \pi \times 30^2 \times 36\) or 14123 – 14151 | M1 |
| \(\text{“}\pi \times 30^2 \times 5\text{”} = \frac{4}{3}\pi r^3\) | M1 |
| \(r^3 = \dfrac{3 \times \text{“}\pi \times 30^2 \times 5\text{”}}{4\pi}\) or \(\dfrac{15 \times 30^2}{4}\) | M1 |
| \(\sqrt[3]{\dfrac{3 \times \text{“}\pi \times 30^2 \times 5\text{”}}{4\pi}}\) oe | M1 |
| 15 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: dep on previous M1
M1: dep on previous M1
M1: dep on previous M1
A1: for 15 or for answer rounding to 15.0