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Answer 1

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Problem:

• What is the volume of this rectangular prism?

Formula for volume (v):

`\quad\quad\quad\quad \boxed{\tt{v = lwh}}`

Given that:

`\quad\quad\quad\quad\tt{length (l)= 9y}`

`\quad\quad\quad\quad\tt{width(w)= 7y}`

`\quad\quad\quad\quad\tt{height(h)= 6y}`

Solution:

`\quad\quad\quad\quad\tt{v = lwh}`

`\quad\quad\quad\quad\tt{v = (9y)(7y)(6y)}`

`\quad\quad\quad\quad\tt{v = (9y)(42 {y}^(2)) }`

`\quad\quad\quad\quad \underline{\tt{v = 378 {y}^(3) }}`

Hence, the final answer is:

`\quad\quad\quad\quad \underline { \boxed{\tt{ \color{magenta}v = 378 {y}^(3) }}}`

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Answer 2

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

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