# Volume: The volume V of a cone is given by V = (1/3) Pi r^2h

#### REGINA

##### New member
The volume V of a cone is given by V = (1/3) Pi r^2 h where r is the radius of the cone and h is its height. What would be the expression that gives r in terms of V and h?

#### Mrspi

##### Senior Member
Re: VOLUME

REGINA said:
The volume V of a cone is given by V=1/3Pie r^2h where r is the radius of the cone and h is its height. What would be the expression that gives r in terms of V and h?
You've got

V = (1/3) pi r<SUP>2</SUP> h

We'll solve this for r. Start by multiplying both sides of the equation by 3 to eliminate the fraction:

3*V = 3*(1/3) pi r<SUP>2</SUP> h

3V = pi r<SUP>2</SUP> h

Now, we want to get rid of the pi and h that are MULTIPLIERS on the right side. Divide both sides of the equation by pi h:

(3V) / (pi h) = (pi r<SUP>2</SUP> h) / (pi h)

(3V) / (pi h) = r<SUP>2</SUP>

To finish, take the square root of both sides of the equation.....