4MA0 Higher June 2014 Paper 4 Q21
21 A sphere has a surface area of \(81\pi\) cm2.
Work out the volume of the sphere.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| \(4\pi r^2 = 81\pi\) or \(4r^2 = 81\) | M1 |
| \(r = \sqrt{\dfrac{81\pi}{4\pi}}\) (=4.5) | M1 |
| \(\dfrac{4}{3} \times \pi \times \text{“}4.5\text{”}^3\) | M1 |
| 382 | A1 |
| (4 marks) |
Notes
M1: ft for “r” dep on first M1
A1: for 381 - 382
M2 for \(r = 4.5\) or \(r = \sqrt{\dfrac{81\pi}{4\pi}}\) oe (may be seen in two stages)