Math / Geometry

QuestionA rectangular bin has the following dimensions. Write a formula that represents the volume, V , of the bin. $V=$ $\square$ (Simplify your answer. Do not factor.)

Studdy Solution

STEP 1

What is this asking? We need to find a simplified formula for the volume of a rectangular bin given its length, width, and height. Watch out! Don't forget to simplify the formula completely by distributing and combining like terms!

STEP 2

1. Define the formula
2. Substitute the dimensions
3. Simplify the formula

STEP 3

Alright, let's start with the basics!
The volume $V$ of a rectangular bin is given by the formula: $V = l \cdot w \cdot h$ where $l$ is the length, $w$ is the width, and $h$ is the height of the bin.
Easy peasy, right?

STEP 4

Now, let's plug in the given dimensions!
We have $l = x + 12$ , $w = 8x$ , and $h = 5x$ .
Substituting these values into our volume formula, we get: $V = (x + 12) \cdot (8x) \cdot (5x)$ Looking good so far!

STEP 5

Time to flex our algebra muscles!
First, let's multiply $8x$ and $5x$ together: $8x \cdot 5x = 40x^2$ So, our formula becomes: $V = (x + 12) \cdot 40x^2$

STEP 6

Now, we distribute $40x^2$ to both terms inside the parentheses: $V = 40x^2 \cdot x + 40x^2 \cdot 12$

STEP 7

Finally, we simplify each term: $V = 40x^3 + 480x^2$ And there we have it!
Our simplified formula for the volume of the rectangular bin.

STEP 8

The volume of the bin is given by the formula $V = 40x^3 + 480x^2$ .

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QuestionA rectangular bin has the following dimensions. Write a formula that represents the volume, V , of the bin. $V=$ $\square$ (Simplify your answer. Do not factor.)

Studdy Solution

STEP 1

What is this asking? We need to find a simplified formula for the volume of a rectangular bin given its length, width, and height. Watch out! Don't forget to simplify the formula completely by distributing and combining like terms!

STEP 2

1. Define the formula
2. Substitute the dimensions
3. Simplify the formula

STEP 3

Alright, let's start with the basics!
The volume $V$ of a rectangular bin is given by the formula: $V = l \cdot w \cdot h$ where $l$ is the length, $w$ is the width, and $h$ is the height of the bin.
Easy peasy, right?

STEP 4

Now, let's plug in the given dimensions!
We have $l = x + 12$ , $w = 8x$ , and $h = 5x$ .
Substituting these values into our volume formula, we get: $V = (x + 12) \cdot (8x) \cdot (5x)$ Looking good so far!

STEP 5

Time to flex our algebra muscles!
First, let's multiply $8x$ and $5x$ together: $8x \cdot 5x = 40x^2$ So, our formula becomes: $V = (x + 12) \cdot 40x^2$

STEP 6

Now, we distribute $40x^2$ to both terms inside the parentheses: $V = 40x^2 \cdot x + 40x^2 \cdot 12$

STEP 7

Finally, we simplify each term: $V = 40x^3 + 480x^2$ And there we have it!
Our simplified formula for the volume of the rectangular bin.

STEP 8

The volume of the bin is given by the formula $V = 40x^3 + 480x^2$ .

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QuestionA rectangular bin has the following dimensions. Write a formula that represents the volume, V , of the bin. V=V=V= □\square□ (Simplify your answer. Do not factor.)

Studdy Solution

STEP 1

What is this asking? We need to find a simplified formula for the volume of a rectangular bin given its length, width, and height. Watch out! Don't forget to simplify the formula completely by distributing and combining like terms!

STEP 2

1. Define the formula2. Substitute the dimensions3. Simplify the formula

STEP 3

Alright, let's start with the basics!The volume VVV of a rectangular bin is given by the formula: V=l⋅w⋅h V = l \cdot w \cdot h V=l⋅w⋅h where lll is the length, www is the width, and hhh is the height of the bin.Easy peasy, right?

STEP 4

Now, let's plug in the given dimensions!We have l=x+12l = x + 12l=x+12, w=8xw = 8xw=8x, and h=5xh = 5xh=5x.Substituting these values into our volume formula, we get: V=(x+12)⋅(8x)⋅(5x) V = (x + 12) \cdot (8x) \cdot (5x) V=(x+12)⋅(8x)⋅(5x) Looking good so far!

STEP 5

Time to flex our algebra muscles!First, let's multiply 8x8x8x and 5x5x5x together: 8x⋅5x=40x2 8x \cdot 5x = 40x^2 8x⋅5x=40x2 So, our formula becomes: V=(x+12)⋅40x2 V = (x + 12) \cdot 40x^2 V=(x+12)⋅40x2

STEP 6

Now, we distribute 40x240x^240x2 to both terms inside the parentheses: V=40x2⋅x+40x2⋅12 V = 40x^2 \cdot x + 40x^2 \cdot 12 V=40x2⋅x+40x2⋅12

STEP 7

Finally, we simplify each term: V=40x3+480x2 V = 40x^3 + 480x^2 V=40x3+480x2 And there we have it!Our simplified formula for the volume of the rectangular bin.

STEP 8

The volume of the bin is given by the formula V=40x3+480x2V = 40x^3 + 480x^2V=40x3+480x2.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionA rectangular bin has the following dimensions. Write a formula that represents the volume, V , of the bin. $V=$ $\square$ (Simplify your answer. Do not factor.)

1. Define the formula
2. Substitute the dimensions
3. Simplify the formula

Alright, let's start with the basics!
The volume $V$ of a rectangular bin is given by the formula: $V = l \cdot w \cdot h$ where $l$ is the length, $w$ is the width, and $h$ is the height of the bin.
Easy peasy, right?

Now, let's plug in the given dimensions!
We have $l = x + 12$ , $w = 8x$ , and $h = 5x$ .
Substituting these values into our volume formula, we get: $V = (x + 12) \cdot (8x) \cdot (5x)$ Looking good so far!

Time to flex our algebra muscles!
First, let's multiply $8x$ and $5x$ together: $8x \cdot 5x = 40x^2$ So, our formula becomes: $V = (x + 12) \cdot 40x^2$

Now, we distribute $40x^2$ to both terms inside the parentheses: $V = 40x^2 \cdot x + 40x^2 \cdot 12$

Finally, we simplify each term: $V = 40x^3 + 480x^2$ And there we have it!
Our simplified formula for the volume of the rectangular bin.

The volume of the bin is given by the formula $V = 40x^3 + 480x^2$ .