A solid ball is exactly fitted inside the cubical box of side \(a\). The volume of the ball is \(\dfrac{4}{3}\pi a^3\).
Step 1: The ball fits exactly inside the cube. This means the diameter of the ball is equal to the side of the cube. So, diameter of ball = \(a\) (in metres, SI unit).
Step 2: Radius is half of diameter. Therefore, radius \(r = \dfrac{a}{2}\, \text{m}\).
Step 3: Formula for volume of a sphere (ball) is: \[ V = \dfrac{4}{3} \pi r^3 \]
Step 4: Substitute \(r = a/2\): \[ V = \dfrac{4}{3} \pi \left(\dfrac{a}{2}\right)^3 = \dfrac{4}{3} \pi \cdot \dfrac{a^3}{8} = \dfrac{\pi a^3}{6} \]
Step 5: The question states that the volume is \(\dfrac{4}{3}\pi a^3\). But we found the actual volume is \(\dfrac{\pi a^3}{6}\).
Final Answer: Since the given volume is incorrect, the statement is False.