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The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box?

Respuesta :

BlueSky06
We are asked to solve for the expression that would represent the volume of the box. The given side measurements of the rectangular prism box are enumerated below:
L = 2a + 11
W = (5a-12)
H = (a+6)

The formula and solution are shown below:
Volume = LWH
Volume = (2a + 11)(5a -12)(a+6)
Volume = (10a²-24a +55a - 132)(a+6)
              = (10a² + 31a - 132) (a + 6)
              = (10³ +31a² -132a + 60a² + 186a - 792)
               = 10a³ +91a² +54a - 792

The answer is 10a³ + 91a² + +54a -792.
ernikhil

The expression for the volume of the rectangular box is [tex]V=10a^3 +91a^2 +54a - 792[/tex].

According to the question, the volume of the rectangular prism is given as [tex]V=l\times w\times h[/tex] where, [tex]l[/tex] is the length of the prism, [tex]w[/tex] is the width, and [tex]h[/tex] is the height of the rectangular prism.

The dimensions of the rectangular box is-

[tex]l=2a+11\\w=5a-12\\h=a+6[/tex]

Substitute the expressions of the parameters in the formula of the volume as-

[tex]V=l\times w\times h\\V=(2a+11)\times (5a-12)\times (a+6)\\V=10a^3 +91a^2 +54a - 792[/tex]

Hence, the expression for the volume of the rectangular box is [tex]V=10a^3 +91a^2 +54a - 792[/tex].

Learn more about rectangular prism here:

https://brainly.com/question/21308574

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