Question

The base of a box is a rectangle. The width of the box is half its length. The height of the box is 0.5m. Find the volume of the box if the area of the base is 1.08m² less than the combined area of the sides.

(There are multiple answers)

Answer 1

Answer: 0.81
`m^3` or 0.36
`m^3`

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

⇒
`3l/2 - l^2/2 = 1.08`

⇒
`3l-l^2=2.16`

⇒
`l^2-3l+2.16=0`

⇒ 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
`m^3` or 0.81
`m^3`