A marble is spherical in shape with a radius of 4 cm. If the marble is placed inside a cube with side length 10 cm, what is the volume of the cube that is not occupied by the marble?

Correct — B. Empty space = cube's volume − marble's volume. The marble is 8 cm across, so it fits inside the 10 cm cube.

Cube volume = 10³ = 1000 cm³
Marble volume = (4⁄3)πr³ = (4⁄3) × 3.14 × 4³
= (4⁄3) × 3.14 × 64 ≈ 267.95 cm³

Subtract: 1000 − 267.95 ≈ 732.05 cm³
Nearest, and printed as 732.06 cm³ → option (b)

Why the others are wrong

• (a)
  100 cm³ — 100 cm³ empty would leave the marble 900 cm³. That needs a radius of about 6 cm, a 12 cm ball that could not fit in a 10 cm cube.
• (c)
  300 cm³ — 300 cm³ empty means a 700 cm³ marble, radius about 5.5 cm. That ball is 11 cm across, wider than the cube, and the stem's radius is 4 cm.
• (d)
  624.82 cm³ — 624.82 cm³ empty needs a marble of about 375 cm³, a radius near 4.47 cm. A 4 cm marble fills only about 268 cm³.

Unoccupied volume = container − object, as long as the object sits fully inside. The marble's diameter is 8 cm and the cube's side is 10 cm, so it fits.

The sphere formula is V = (4⁄3)πr³. Because r is cubed, the radius drives the answer: r = 4 puts 64 in the formula, r = 5 would put 125.

The options sit more than 100 cm³ apart, so π = 3.14 and π = 22⁄7 both point to the same one.

Key facts

• Volume of a sphere = (4⁄3)πr³, which is 256π⁄3 cm³ for r = 4 cm.
• Volume of a cube = a³, so a 10 cm cube holds 1000 cm³.
• A sphere fits inside a cube only if its diameter, 2r, is no more than the cube's side.

Common traps

• Using the diameter, 8 cm, as r: (4⁄3) × 3.14 × 512 ≈ 2,144 cm³, more than the whole cube.
• Dropping the 4⁄3: π × 4³ ≈ 201 cm³ leaves about 799 cm³, which matches no option.

No directly related past PYQ was found.