Answer:
Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.
Step-by-step explanation:
Cuboid : A cuboid is a three dimension shape. The length ,breadth and height of a cuboid are not same.
- A cuboid has 6 faces.
- A cuboid contains 8 vertices.
- A cuboid contains 12 edges .
- The total surface area of a cuboid is
= 2(length×breadth+breadth×height+length×height) square units
- The dimension of a cuboid is written as length×breadth×height.
- The volume is( length×breadth×height) cubic units
Given that the volume of the box is 192 cubic inches.
Let x inches be the width of the cuboid.
Since the length is twice as long as its width.
Then length = 2x inches
Again height is 2 inches longer than width.
Then height = (x+2) inches.
Therefore the volume of the cuboid is
cubic inches
cubic inches
cubic inches
According to the problem,
![2x^3+4x^2=192](https://tex.z-dn.net/?f=2x%5E3%2B4x%5E2%3D192)
![\Rightarrow 2x^3+4x^2-192=0](https://tex.z-dn.net/?f=%5CRightarrow%202x%5E3%2B4x%5E2-192%3D0)
![\Rightarrow 2(x^3+2x^2-96)=0](https://tex.z-dn.net/?f=%5CRightarrow%202%28x%5E3%2B2x%5E2-96%29%3D0)
![\Rightarrow (x^3+2x^2-96)=0](https://tex.z-dn.net/?f=%5CRightarrow%20%28x%5E3%2B2x%5E2-96%29%3D0)
![\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0](https://tex.z-dn.net/?f=%5CRightarrow%20x%5E3-4x%5E2%2B6x%5E2-24x%2B24x-96%3D0)
![\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0](https://tex.z-dn.net/?f=%5CRightarrow%20x%5E2%28x-4%29%20%2B6x%28x-4%29%2B24%28x-4%29%3D0)
![\Rightarrow (x-4)(x^2+6x+24)=0](https://tex.z-dn.net/?f=%5CRightarrow%20%28x-4%29%28x%5E2%2B6x%2B24%29%3D0)
Therefore x=4
Since the all zeros of x²+6x+24 =0 is negative.
Therefore breadth = 4 inches
length=(2×4) inches=8 inches
and height = (4+2)inches = 6 inches.
Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.