Moderate -0.5 This is a straightforward algebraic rearrangement requiring squaring both sides, expanding, collecting terms, and taking a square root. While it involves multiple steps and manipulation of a square root, it follows a standard procedure with no conceptual difficulty or problem-solving insight required—slightly easier than average for A-level.
8 The volume \(V\) of a cone with base radius \(r\) and slant height \(l\) is given by the formula
$$V = \frac { 1 } { 3 } \pi r ^ { 2 } \sqrt { l ^ { 2 } - r ^ { 2 } }$$
Rearrange this formula to make \(l\) the subject.
For correctly getting non-'\(l^2 - r^2\)' terms on other side [M0 for 'triple decker' fraction]; may be done in several steps, condone omission of brackets
Mark final answer; for finding square root and dealing correctly with coefficient of \(l\) term if needed; condone \(\pm\sqrt{\text{etc}}\); For M4, final expression must be totally correct [condoning omission of \(l\) and insertion of \(\pm\)]; eg M4 for \(\dfrac{\sqrt{9V^2 + \pi^2 r^6}}{\pi r^2}\)
## Question 8:
$\dfrac{3V}{\pi r^2} = \sqrt{l^2 - r^2}$ | M1 | For correctly getting non-'$l^2 - r^2$' terms on other side [M0 for 'triple decker' fraction]; may be done in several steps, condone omission of brackets
$\left(\dfrac{3V}{\pi r^2}\right)^2 = l^2 - r^2$ | M1 (oe or ft) | For squaring correctly; for combined steps allow credit for correct process where possible eg $\pi^2 r^4 l^2$ as the term on one side
$l^2 = \left(\dfrac{3V}{\pi r^2}\right)^2 + r^2$ | M1 (oe or ft) | For getting $l$ term as subject
$[l =]\sqrt{\left(\dfrac{3V}{\pi r^2}\right)^2 + r^2}$ | M1 (oe or ft) | Mark final answer; for finding square root and dealing correctly with coefficient of $l$ term if needed; condone $\pm\sqrt{\text{etc}}$; For M4, final expression must be totally correct [condoning omission of $l$ and insertion of $\pm$]; eg M4 for $\dfrac{\sqrt{9V^2 + \pi^2 r^6}}{\pi r^2}$
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8 The volume $V$ of a cone with base radius $r$ and slant height $l$ is given by the formula
$$V = \frac { 1 } { 3 } \pi r ^ { 2 } \sqrt { l ^ { 2 } - r ^ { 2 } }$$
Rearrange this formula to make $l$ the subject.
\hfill \mbox{\textit{OCR MEI C1 Q8 [4]}}