A cubical box with an inside edge of 30 cm is filled completely with ice cubes of edge 1 cm. How many ice cubes does it hold?

Class 8Cubes and Cube RootsCubes and Roots

A90
B900
C27000
D2700

Step-by-Step Solution

The box holds

3 0^{3} = 30 \times 30 \times 30 = 27000

cubes of

1 cm^{3}

each. The option 900 is only

3 0^{2}

, which counts a single layer — there are 30 such layers stacked up.

Answer: C) 27000

Key idea: Estimating cube roots

For non-perfect cubes, bracket the cube root between two consecutive integers.

Example: ∛100. We know

4^{3} = 64

and

5^{3} = 125

. So 4 < ∛100 < 5. Closer to 5 (100 is closer to 125 than 64). Refined estimate: ∛100 ≈ 4.64.

For perfect cubes, look at the last digit (last digit rule for cubes: each digit cubes to a unique last digit). 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9, 0→0.

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