Q.1. The length of a cuboidal box made of coloured paper is three units greater than the width, and its height is two units less than the width, if width is taken as x, answer the following questions. i) Select the polynomial that represents volume of the box*1 point4x² + 2x + 46x² + 4x-12x^3+x^2-6x5x^2 + 3x -12
Question
Q.1. The length of a cuboidal box made of coloured paper is three units greater than the width, and its height is two units less than the width, if width is taken as x, answer the following questions. i) Select the polynomial that represents volume of the box*1 point4x² + 2x + 46x² + 4x-12x^3+x^2-6x5x^2 + 3x -12
Solution
The volume of a cuboid is given by the formula length * width * height.
Given that the length is three units greater than the width, we can represent the length as (x + 3).
The height is two units less than the width, so we can represent the height as (x - 2).
The width is given as x.
So, the volume V of the cuboid can be represented as:
V = length * width * height V = (x + 3) * x * (x - 2)
If we expand this, we get:
V = x * (x^2 - 2x + 3x - 6) V = x * (x^2 + x - 6) V = x^3 + x^2 - 6x
So, the polynomial that represents the volume of the box is x^3 + x^2 - 6x.
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