Calculate Building Volume: Find Expression for 21×15×(14+30X) Meters³

Volume Calculation with Algebraic Expressions

A building is 21 meters high, 15 meters long, and 14+30X meters wide.

Express its volume in terms of X.

(14+30X)(14+30X)(14+30X)212121151515

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

A building is 21 meters high, 15 meters long, and 14+30X meters wide.

Express its volume in terms of X.

(14+30X)(14+30X)(14+30X)212121151515

2

Step-by-step solution

We use a formula to calculate the volume: height times width times length.

We rewrite the exercise using the existing data:

21×(14+30x)×15= 21\times(14+30x)\times15=

We use the distributive property to simplify the parentheses.

We multiply 21 by each of the terms in parentheses:

(21×14+21×30x)×15= (21\times14+21\times30x)\times15=

We solve the multiplication exercise in parentheses:

(294+630x)×15= (294+630x)\times15=

We use the distributive property again.

We multiply 15 by each of the terms in parentheses:

294×15+630x×15= 294\times15+630x\times15=

We solve each of the exercises in parentheses to find the volume:

4,410+9,450x 4,410+9,450x

3

Final Answer

4410+9450x 4410+9450x

Key Points to Remember

Essential concepts to master this topic
  • Formula: Volume equals height × width × length for rectangular shapes
  • Technique: Apply distributive property: 21 × (14 + 30X) = 294 + 630X
  • Check: Substitute X value to verify: when X=1, volume = 4410+9450(1) = 13,860 m³ ✓

Common Mistakes

Avoid these frequent errors
  • Adding dimensions instead of multiplying them
    Don't calculate 21 + 15 + (14 + 30X) = 50 + 30X for volume! This gives perimeter-like results, not volume. Always multiply all three dimensions: height × width × length to get cubic units.

Practice Quiz

Test your knowledge with interactive questions

Calculate the volume of the rectangular prism below using the data provided.

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FAQ

Everything you need to know about this question

Why do I need to multiply all three dimensions?

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Volume measures the space inside a 3D shape. To fill that space, you need length × width × height. Think of it as stacking unit cubes - you need all three directions!

When do I use the distributive property?

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Use distributive property when you have parentheses with addition or subtraction inside. Here, multiply 21 by both terms: 21×14 21 \times 14 and 21×30X 21 \times 30X .

What does the X represent in this problem?

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X is a variable representing an unknown measurement that affects the building's width. The width changes based on X's value, making the volume depend on X.

How do I know my final expression is correct?

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Your answer should have two terms: a constant (4410) and a term with X (9450X). Check by substituting a simple value like X=0 or X=1 into your expression.

Why is the answer in cubic meters?

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Since all dimensions are in meters, volume is in cubic meters (m³). When you multiply three lengths together, you get cubic units - that's how volume is always measured!

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