If the base area of a right circular cone is \(A\), its height is \(H\), and its volume is \(V\), then express \(H\) in terms of \(V\) and \(A\).

Q.If the base area of a right circular cone is \(A\), its height is \(H\), and its volume is \(V\), then express \(H\) in terms of \(V\) and \(A\). (a) \(H=\cfrac{3V}{A}\) (b) \(H=\cfrac{V}{A}\) (c) \(H=\cfrac{V}{3A}\) (d) \(H=\cfrac{3V}{2A}\)

Answer: A

We know, Volume of a cone = \(\frac{1}{3} \times\) base area \(\times\) height i.e., \(V = \frac{1}{3}AH\) i.e., \(AH = 3V\) i.e., \(H = \frac{3V}{A}\)