B

Step 1: Understand the physical properties affected by temperature changes. When the temperature of a metal ball increases, it expands. The key relationships for a sphere involving volume $V$, surface area $A$, and radius $r$ are as follows:
- Volume: $V = \frac{4}{3} \pi r^3$
- Surface Area: $A = 4 \pi r^2$
- Radius: $r$

Step 2: Analyze how each property changes with temperature:
- The radius of the sphere increases linearly with temperature due to thermal expansion. For small temperature changes, the radius change is represented as:
$$ r' = r (1 + \alpha \Delta T) $$
Here, $\alpha$ is the coefficient of linear expansion, and $\Delta T$ is the change in temperature. The percentage change in radius is approximately $\Delta r / r = \alpha \Delta T$.

- The surface area changes:
$$ A' = 4\pi (r')^2 = 4\pi [r (1 + \alpha \Delta T)]^2 = 4\pi r^2(1 + \alpha \Delta T)^2 $$
For small changes, we can approximate the percentage change in surface area as $\Delta A / A \approx 2\alpha \Delta T$.

- The volume changes:
$$ V' = \frac{4}{3}\pi (r')^3 = \frac{4}{3}\pi [r(1 + \alpha \Delta T)]^3 = \frac{4}{3}\pi r^3(1 + \alpha \Delta T)^3 $$
For small changes, the percentage change in volume is approximately $\Delta V / V \approx 3\alpha \Delta T$.

Step 3: Collate the percentage changes:
- Change in radius: $\alpha \Delta T$
- Change in surface area: $2\alpha \Delta T$
- Change in volume: $3\alpha \Delta T$

Step 4: Order the percentage changes in ascending order:
- Radius change: $\alpha \Delta T$
- Surface area change: $2\alpha \Delta T$
- Volume change: $3\alpha \Delta T$

The ascending order is: radius < surface area < volume. Thus, the correct answer corresponds to option B.