Find X in a Cuboid: Volume 924 with Dimensions 12 and 7

Q: What's the difference between area and volume formulas?

Area uses 2 dimensions (length × width), but volume uses 3 dimensions (length × width × height). Since this is a 3D cuboid, we multiply all three measurements.

Q: Why do I multiply 12 × 7 first?

It's easier to simplify! Calculate $ 12 \times 7 = 84 $ first, then solve $ 924 = 84 \times X $. This makes the division much simpler.

Q: How do I check if 924 ÷ 84 = 11?

Use multiplication to check division: $ 11 \times 84 = 924 $. You can also verify that $ 11 \times 12 \times 7 = 924 $.

Q: What if I can't divide 924 by 84 easily?

Break it down! $ 84 \times 10 = 840 $, so you need $ 924 - 840 = 84 $ more. Since $ 84 \times 1 = 84 $, the answer is 10 + 1 = 11.

Q: Could X be a decimal number?

In this problem, X = 11 is a whole number, which makes sense for cuboid dimensions. Always check if your answer is reasonable for the context!

Volume Formula with Unknown Dimension

The volume of the cuboid is 924.

What is the value of X?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the height of box X

00:03 We'll use the formula for calculating box volume

00:07 width times height times length

00:11 We'll substitute appropriate values according to the given data and solve for X

00:34 We'll isolate X

00:43 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The volume of the cuboid is 924.

What is the value of X?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Apply the formula for the volume of a cuboid: $V = l \times w \times h$ .
Step 2: Substitute the known values: $924 = 12 \times 7 \times X$ .
Step 3: Simplify and solve for $X$ .

Now, let's work through each step:
Step 1: The formula for the volume of the cuboid is $V = l \times w \times h$ .
Step 2: Substitute the given values into the formula: $924 = 12 \times 7 \times X$ .
Step 3: Calculate $12 \times 7$ which equals 84. Thus, $924 = 84 \times X$ .
Step 4: Solve for $X$ by dividing both sides by 84:
$\frac{924}{84} = X$
Perform the division: $924 \div 84 = 11$ .

Therefore, the value of $X$ is $11$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cuboid equals length times width times height
Technique: Substitute known values: 924 = 12 × 7 × X
Check: Verify 11 × 12 × 7 = 924 ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't calculate 12 + 7 + X = 924 because addition gives perimeter, not volume! This leads to X = 905, which is impossibly large for a cuboid dimension. Always multiply all three dimensions for volume.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

What's the difference between area and volume formulas?

Area uses 2 dimensions (length × width), but volume uses 3 dimensions (length × width × height). Since this is a 3D cuboid, we multiply all three measurements.

Why do I multiply 12 × 7 first?

It's easier to simplify! Calculate $12 \times 7 = 84$ first, then solve $924 = 84 \times X$ . This makes the division much simpler.

How do I check if 924 ÷ 84 = 11?

Use multiplication to check division: $11 \times 84 = 924$ . You can also verify that $11 \times 12 \times 7 = 924$ .

What if I can't divide 924 by 84 easily?

Break it down! $84 \times 10 = 840$ , so you need $924 - 840 = 84$ more. Since $84 \times 1 = 84$ , the answer is 10 + 1 = 11.

Could X be a decimal number?

In this problem, X = 11 is a whole number, which makes sense for cuboid dimensions. Always check if your answer is reasonable for the context!

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Find X in a Cuboid: Volume 924 with Dimensions 12 and 7

Volume Formula with Unknown Dimension

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What's the difference between area and volume formulas?

Why do I multiply 12 × 7 first?

How do I check if 924 ÷ 84 = 11?

What if I can't divide 924 by 84 easily?

Could X be a decimal number?

🌟 Unlock Your Math Potential

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