Final answer:
The positive value of the radius (r) is specified because a negative radius doesn't make sense for a real object. To solve for the positive r, rearrange the volume formula, V = πr²h, as r = √(V/πh) and substitute the values for V and h.
Step-by-step explanation:
The question focuses on finding the positive value of the radius (r) of a cylinder when you know the volume (V) and the height (h) of the cylinder, using the formula V = πr²h. The specification of the positive value of r is necessary because in mathematics, particularly in the context of geometry, only non-negative values make sense for lengths and distances. A negative radius would not be meaningful for a real, physical cylinder.
To find the radius of the cylinder in terms of V and h, we rearrange the formula to solve for r: r = √(V/πh). Substitute the given values for V and h into the formula to calculate r. Remember that the square root function can return both positive and negative values, but we only take the positive value since it's the only one that is physically significant for a radius.
For example, if V = 9.278 cm³ and h = 5.25 cm, you would calculate the radius r as follows: r = √(9.278 cm³ / (π × 5.25 cm)) which gives the radius in centimeters. Always ensure you use the correct units and calculate the value accurately based on the formula provided.