Question

the volume of the cone is given by the formula V = 1/3 pie r^2 h, where r is the radius of the base and h is the height of the cone. based on this formula, whatis the height, h, of the cone in terms of the volume and height

answer is h=3v/pie r^2. need help with showing work​

Answer 1

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Answer:

  h = 3V/(πr²)

Step-by-step explanation:

The formula can be solved for h by multiplying both sides by the inverse of the coefficient of h.

  $V=\dfrac{1}{3}\pi r^2h=\dfrac{\pi r^2}{3}h\\\\(\dfrac{3}{\pi r^2})V=(\dfrac{3}{\pi r^2})(\dfrac{\pi r^2}{3})h\\\\\boxed{\dfrac{3V}{\pi r^2}=h}$

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Additional comment

Whenever a variable has a coefficient you don't want, you can make that be 1 by multiplying the equation by the inverse of the coefficient. This is the same as dividing by the coefficient. This makes use of the fact that for any non-zero 'a', the ratio a/a has a value of 1. Anything multiplied by 1 is unchanged.

  V = ah   ⇒   V/a = (ah)/a = h(a/a) = h·1 = h

Note that we multiply the whole equation (both sides of the equal sign) by 1/a. The basic rule of equality is that you can do whatever you like to an equation, as long as you do it to both sides.