Question

The equation for the volume of a cylinder is V = πr^2h. The positive value of r, in terms of h and V is:

Answer 1

The positive value of the radius r, in terms of the height h and the volume V of a cylinder, is calculated by rearranging the formula V = πr^2h to r = √(V / (πh)). This is done by dividing both sides of the equation by πh and then taking the square root.

Step-by-step explanation:

The student has asked for the positive value of r, the radius of a cylinder, in terms of h, the height of the cylinder, and V, the volume of the cylinder. The equation for the volume of a cylinder is given by V = πr^2h. To find r in terms of h and V, we rearrange the formula to solve for r:

r = √(V / (πh))

Steps to Solve for r:

1. Divide both sides of the equation by πh: V / (πh) = r^2
2. Take the square root of both sides to solve for r: √(V / (πh)) = r

Here, we used the fact that the volume V is equal to the product of the base area πr^2 and the height h, and to isolate r, we performed algebraic manipulations by dividing and taking square roots.