Question

The height of a rectangular prism is 2 . The width is 4x-1, and its length is 3x^(2)+2x-1. Find the volume.

Answer 1

Explanation:

Given:

1. Height = 2 (units)
2. Width = 4x-1 (units)
3. Length = 3x^(2)+2x-1 (units)

The formula for the volume of rectangular prism is :

Volume = (Length) × (Width) × (Height)

Substituting the expressions (Given), we get

Volume = {[3x^(2)+2x-1] × (4x-1) × 2 } cubic units

Taking first two equations, we get,

Volume = {[3x^(2)+2x-1] × (4x-1)} × 2

Note [ we have multiplied 4x with 3x^(2)+2x-1 then -1 with 3x^(2)+2x-1 )

Solving we get,

Volume = [12x^(3)+5x^(2)-6x+1] x 2

Now, multiplying by 2(i.e. the height) we get,

Volume = 24x^3+10x^2-12x+2 (cubic units)

ANS = 24x^3+10x^2-12x+2 (cubic units)

Answer 2

Answer: The volume of a rectangular prism is calculated by multiplying its length, width, and height. Given that the height is 2, the width is 4x-1, and the length is 3x^2+2x-1, the volume can be determined as follows:

Explanation:

Volume = height × width × length

= 2 × (4x-1) × (3x^2+2x-1)

= 2 × (12x^3 + 8x^2 - 3x^2 - 2x - 3x + 2)

= 2 × (12x^3 + 5x^2 - 5x + 2)

= 24x^3 + 10x^2 - 10x + 4

Thus, the volume of the rectangular prism is given by the polynomial expression 24x^3 + 10x^2 - 10x + 4.