The sum of the lengths of all edges of a rectangular parallelepiped is 144 cm. If its length, breadth, and height are in the ratio 3:2:1, what is its volume?
Show answer & explanation
Correct answer: C
Explanation
Sum of the lengths of all edges = 144 cm
Ratio l : b : h = 3 : 2 : 1
Total edges = 4(l + b + h)
4(l + b + h) = 144
l + b + h = 36
Let
l = 3x, b = 2x, h = x
3x + 2x + x = 6x = 36
x = 6
l = 18, b = 12, h = 6
Volume = l × b × h = 18 × 12 × 6 = 1296 cm³