Respuesta :
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
[tex]=[x\times 2x\times (x+2)][/tex] cubic inches
[tex]=[2x^2(x+2)][/tex] cubic inches
[tex]=(2x^3+4x^2)[/tex] cubic inches
According to the problem,
[tex]2x^3+4x^2=192[/tex]
[tex]\Rightarrow 2x^3+4x^2-192=0[/tex]
[tex]\Rightarrow 2(x^3+2x^2-96)=0[/tex]
[tex]\Rightarrow (x^3+2x^2-96)=0[/tex]
[tex]\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0[/tex]
[tex]\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0[/tex]
[tex]\Rightarrow (x-4)(x^2+6x+24)=0[/tex]
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.
