Find the volume of the cube ABCDA1B1C1D1 if DE = 1 cm, where E is the midpoint of the edge AB.

univerkov | December 16, 2020 | education

V ABCDA1B1C1D1—?
DE² = AD² + AE² = 2AE² + AE² = 3AE² = 1
AE = 1/3 → AB = 2 AE = 2 × 1 ÷ 3 = 2/3 (cm) – side of the cube.
V = a³
V = (2/3) ³ = 8/27 (cm³)
Answer: V = 8/27 cm³.

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