Rearranging formula - multi-step isolation with nested operations

Rearrange a formula where the target variable appears once but is embedded in nested operations requiring multiple steps to isolate, such as T = 2π√(l/g), c = √((a+b)/2), a = (√y - 5)/c, or V = ⅓πr²√(l²-r²).

4 questions · Moderate -0.9

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OCR MEI C1 Q2

3 marks Moderate -0.8

2 Make \(l\) the subject of the formula \(T = 2 \pi \sqrt { \frac { l } { g } }\).

OCR MEI C1 Q8

4 marks Moderate -0.5

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.

OCR MEI C1 2010 January Q1

3 marks Easy -1.8

1 Rearrange the formula \(c = \sqrt { \frac { a + b } { 2 } }\) to make \(a\) the subject.

OCR MEI C1 2011 January Q5

4 marks Moderate -0.5

5 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.