Answer: 0.81 [tex]m^3[/tex] or 0.36 [tex]m^3[/tex]
Step-by-step explanation:
Let length of the given cuboid = l
Therefore, according to the question,width of the cuboid = l/2
Now, the height of the cuboid = 0.5
Again according to the question,
The area of the base is 1.08m² less than the combined area of the sides.
Therefore, 2(l+l/2) ×0.5 - l×l/2 = 1.08
⇒ [tex]3l/2 - l^2/2 = 1.08[/tex]
⇒ [tex]3l-l^2=2.16[/tex]
⇒ [tex]l^2-3l+2.16=0[/tex]
⇒ l = 1.2 m or 1.8 m
Thus, width of the cuboid = 0.6 m or 0.9 m
⇒ Therefore, the volume of the box, V = 1.2 × 0.6 × 0.5 or 1.8 × 0.9 × 0.5
⇒ V = 0.36 [tex]m^3[/tex] or 0.81 [tex]m^3[/tex]
