Final answer:
The volume of the cuboid, given the ratio of the sides as 4:3:2 and total surface area of 468, is found to be 648 cubic units after determining the value of x in the ratio.
Step-by-step explanation:
The ratio of the length, breadth, and height of a cuboid is 4:3:2, and the total surface area is 468 square units. To find the volume, we can use the dimensions based on the given ratio. Let's represent the length by 4x, breadth by 3x, and the height by 2x. The surface area of a cuboid is given by the formula:
SA = 2(lb + bh + hl)
If we substitute our dimensions into this formula we get:
468 = 2(4x*3x + 3x*2x + 2x*4x)
468 = 2(12x² + 6x² + 8x²)
468 = 2(26x²)
468 = 52x²
x² = 9
x = 3
Now, we can find the volume (V) using the formula:
V = l*b*h
V = 4x*3x*2x
V = 4*3*2*x³
V = 24*x³
V = 24*3³
V = 24*27
V = 648 cubic units
Thus, the volume of the cuboid is 648 cubic units.