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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. Which expression represents the volume of the following rectangular prism?

h=2x+9
l= x+2
w= 3x

A) 2x^2+13x+18
B) 6x^3+27x^2+54x
C) 6x^3+39x^2+54x
D) 18x^4+117x^3+162x^2

Respuesta :

Solution: As given, Volume of a rectangular prism is given by the formula V = l w h, where l is the length of the prism, w is the width, and h is the height.

also , h=2x+9

l= x+2

w= 3 x

So, volume of prism= (2 x+9)(x+2)(3 x)= (3 x)(2 x+9)(x+2)→Using associative property

       =3 x[2 x(x+2)+9(x+2)]→Using (x+a)(x+b)= x(x+a)+a(x+b)=x²+(a+b)x+ab

      = 3 x [ 2 x²+ 4 x+ 9 x+18]

      = 3 x[ 2 x² +13 x+18]

 = (3 x)(2 x²) + (3 x)×(13 x) + (3 x)×(18)→ Using distributive property

= 6 x³+ 39 x² + 54 x → [ use [tex]x^{m} \times x^{n}= x^{m+n}[/tex]

Option (C) is correct.


adioabiola

The expression which represents the volume of the rectangular prism is; Choice C: 6x³+39x²+54x

Volume of a rectangular prism

The volume of the rectangular prism as given is;

  • V = lwh

where, h=2x+9, l= x+2, and w= 3x

Therefore, Volume;

  • V = (2x+9) (x+2)(3x)

  • V = (2x² +13x +18)(3x)

  • V = 6x³+39x²+54x

Read more on volume of rectangular prism;

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