The ratio of the dimensions of a rectangular parallelepiped is 2:3:4. If its volume is 768 cm³, what is its smallest dimension?
Show answer & explanation
Correct answer: A
Explanation
Ratio of dimensions = 2 : 3 : 4
Volume = 768 cm³
Volume = l × b × h
Let the dimensions be 2x, 3x, and 4x.
Volume = 2x × 3x × 4x = 24x³
24x³ = 768
x³ = 768 ÷ 24 = 32
x = ∛32
Smallest dimension = 2x = 2∛32 ≈ 2 × 3.2 = 6.34 cm