WAEC 2014 Mathematics · Question 15

The volume of a cube is 512cm3. Find the length of its side

Options

A.6cm
B.7cm
C.8cm
D.9cm

Answer: C. 8cm

Explanation written with AI and checked against the answer key

Analyze the question: We're given the volume of a cube (512 cm³) and need its side length. Concept: All sides of a cube are equal, so its volume is V = s³ where s is the side length. To find s, take the cube root of the volume. Solution: s³ = 512 s = ∛512 Break 512 into prime factors: 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁹ s = ∛(2⁹) = 2³ = 8 Check: 8 × 8 × 8 = 64 × 8 = 512 ✓ Checking the other options: 6³ = 216, 7³ = 343, 9³ = 729, so none of them gives 512. The side length is 8 cm, which is option C. Tip: Memorise the cubes from 1 to 10 (1, 8, 27, 64, 125, 216, 343, 512, 729, 1000). With these, cube-root questions can be answered in seconds. Also, 512 ends in 2, so its cube root must end in 8 (because 8³ ends in 2). That quickly points to 8 or 18, and only 8 is a sensible option here.

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