Understanding Direct Variation

Direct variation means that as one quantity increases, the other quantity increases proportionally. We can express this relationship mathematically as:

* y = kx

Where:

* y is the dependent variable (volume in this case)

* x is the independent variable (temperature)

* k is the constant of proportionality

Solving the Problem

1. Find the Constant of Proportionality (k):

* We know V = 3 L when T = 300 K.

* Substitute these values into the equation: 3 = k * 300

* Solve for k: k = 3 / 300 = 0.01

2. Find the Volume at the New Temperature:

* We want to find V when T = 350 K.

* Use the equation V = kT and substitute the values: V = 0.01 * 350

* Calculate the volume: V = 3.5 L

Answer: The volume of the balloon will rise to 3.5 L when the temperature rises to 350 degrees Kelvin.