Question

A rectangular prism has a Length = 3b - 2 ; Width 4B and a Height of B + 6 Write and simplify a Polynomial expression for the volume of the Rectangular Prism:

Answer 1

Answer:

Given,

Length of a Rectangular Prism = 3b - 2

Breadth of a Rectangular Prism = 4b

Width of a Rectangular Prism = b + 6

To Find :-

Volume of the Rectangular Prism.

Solution :-

let,

Length of the Rectangular Prism be 'l'

Breadth of the Rectangular Prism be 'b'

Height of the Rectangular Prism be 'h'

$Volume \: of \: the \: Rectangular \: Prism = length \times breadth \times height$

$= l \times b \times h$

$volume \: = (3b - 2)(4b)(b + 6)$

$= ((3b - 2) \times 4b) \times (b + 6)$

$= ((3b)4b - (2)4b) \times (b + 6)$

$= (12 {b}^{2} - 8b) \times (b + 6)$

$= (12 {b}^{2} - 8b )b + (12 {b}^{2} - 8b )6$

$= 12 {b}^{3} - 8 {b}^{2} + 72 {b}^{2} - 48b$

$= 12 {b}^{3} + 64 {b}^{2} - 48b$

$\sf\therefore Volume \: of \: the\: Rectangular\:Prism = 12 {b}^{3} \: + 64 {b}^{2} \:- 48b$