November 2021 Paper 2 Q10
10 The radius of a sphere, in cm, is \(\dfrac{3k}{2}\)
The volume of the sphere, in cm\(^3\), is \(972\pi\)
| Volume of a sphere \(= \dfrac{4}{3}\pi r^3 \quad\) where \(r\) is the radius |
Work out the value of \(k\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{4}{3} \times \pi \times \dfrac{27k^3}{8}\) or \(\dfrac{9\pi k^3}{2}\) | M1 | oe |
| \(k^3 = 972 \times 2 \div 9\) or \(k^3 = 216\) or \(\sqrt[3]{216}\) | M1dep | oe eg \(k^3 = 972\pi \times 2 \div 9\pi\) must have \(k^3\) seen or implied |
| 6 | A1 | |
| Alternative method 2 | ||
| \(972\pi \div \dfrac{4}{3}\pi\) or 729 or \(972\pi \div \dfrac{4}{3}\pi\) or 729 or \(\sqrt[3]{729}\) or 9 | M1 | oe eg \((r^3 =)\ 972 \div \dfrac{4}{3}\) |
| \(\dfrac{3k}{2} = \sqrt[3]{\text{their } 729}\) or \(\dfrac{3k}{2} = 9\) or \(9 \times 2 \div 3\) | M1dep | oe must have \(\dfrac{3k}{2}\) seen or implied |
| 6 | A1 | |
Additional guidance
| Alt 1 \(\dfrac{4}{3} \times \dfrac{27k^3}{8}\) is M0 unless recovered | |
| Alt 2 \(972\pi \div \dfrac{4}{3}\) is M0 unless recovered | |
| Alt 1 \(\dfrac{4}{3} \times \pi \times \left(\dfrac{3k}{2}\right)^3\) not subsequently simplified correctly | M0 |