Explanation:

Let’s break it down:

- A sphere passing through all the corners of a cuboid basically means the cuboid’s space diagonal is the diameter of that sphere.

- For a cuboid with sides a, b, c, the space diagonal = v(a² + b² + c²).

- Here, that’s v(8² + 12² + 24²) = v(64 + 144 + 576) = v784 = 28 cm.

- So, the diameter = 28 cm, making the radius half of that, which is 14 cm.

Let’s check each option:

- Option 1: 10.5 cm — Too small, doesn’t fit our diagonal.

- Option 2: 14 cm — This matches our calculation.

- Option 3: 21 cm — That would make the diameter 42 cm, too big.

- Option 4: 28 cm — That refers to the diameter, not the radius.

So, option 2 is the only answer that makes sense.