Respuesta :

Space

Answer:

V = 378y³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Algebra I

  • Terms/Coefficients

Geometry

Volume of a Rectangular Prism: V = lwh

  • l is length
  • w is width
  • h is height

Step-by-step explanation:

Step 1: Define

Identify variables

l = 9y

w = 7y

h = 6y

Step 2: Find Volume

  1. Substitute in variables [Volume of a Rectangular Prism]:                              V = (9y)(7y)(6y)
  2. Multiply:                                                                                                             V = (63y²)(6y)
  3. Multiply:                                                                                                             V = 378y³

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Problem:

  • What is the volume of this rectangular prism?

Formula for volume (v):

[tex]\quad\quad\quad\quad \boxed{\tt{v = lwh}}[/tex]

Given that:

[tex]\quad\quad\quad\quad\tt{length (l)= 9y}[/tex]

[tex]\quad\quad\quad\quad\tt{width(w)= 7y}[/tex]

[tex]\quad\quad\quad\quad\tt{height(h)= 6y}[/tex]

Solution:

[tex]\quad\quad\quad\quad\tt{v = lwh}[/tex]

[tex]\quad\quad\quad\quad\tt{v = (9y)(7y)(6y)}[/tex]

[tex]\quad\quad\quad\quad\tt{v = (9y)(42 {y}^{2}) }[/tex]

[tex]\quad\quad\quad\quad \underline{\tt{v = 378 {y}^{3} }}[/tex]

Hence, the final answer is:

[tex]\quad\quad\quad\quad \underline { \boxed{\tt{ \color{magenta}v = 378 {y}^{3} }}}[/tex]

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