The given formula for the volume of cone can be written as [tex]\sqrt{\frac{2V}{\pi h} }[/tex] in terms of V and h for r.
What is transposing a term in an expression or transpose method?
To bring a term from one side of an equation to the other, with corresponding change in sign or by doing opposite operations is called transposing a term in an expression.
According to the given question.
We have a formula for the volume of cone
[tex]V = \frac{1}{2} \pi r^{2} h[/tex]
To solve the the above formula for r we use transpose method.
Therefore,
[tex]V = \frac{1}{2} \pi r^{2} h[/tex]
⇒ [tex]2V = \pi r^{2}h[/tex] (multiplying by 2 both the sides)
⇒ [tex]\frac{2V}{\pi h} =r^{2}[/tex] (dividing both the sides by πh)
⇒ [tex]r=\sqrt{\frac{2V}{\pi h} }[/tex]
Hence, the given formula for the volume of cone can be written as [tex]\sqrt{\frac{2V}{\pi h} }[/tex] in terms of V and h for r.
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