The length, breadth, and height of a rectangular parallelepiped are in the ratio 2 : 3 : 4. If the total length of all edges is 108 cm, what is the volume of the parallelepiped?
Show answer & explanation
Correct answer: C
Explanation
Given:
Length : Width : Height = 2 : 3 : 4
Total length of all edges = 108 cm
By formula:
Total length of all edges in a parallelogram = 4(l + b + h)
Volume = l × b × h
Let
l = 2x, b = 3x, h = 4x
4(l + b + h) = 108
4(2x + 3x + 4x) = 108
4(9x) = 108
36x = 108
x = 3
l = 6, b = 9, h = 12
Volume = 6 × 9 × 12 = 648 cm³