Calculate Width X in a Cuboid: Given Volume 90, Height 5, Length 3

Q: What's the difference between length, width, and height in a cuboid?

Length, width, and height are just the three dimensions of a rectangular box. It doesn't matter which dimension you call which - the volume formula works the same way regardless!

Q: Why do I multiply all three dimensions together?

Volume measures how much space is inside the cuboid. You need to account for all three directions: length × width × height gives you the total cubic units that fit inside.

Q: What if I get the formula backwards?

No problem! Just rearrange it correctly. If you have $ V = L \times W \times H $, then $ W = \frac{V}{L \times H} $. Division undoes multiplication!

Q: How do I know which dimension is X?

Look at the diagram carefully! The X label shows which dimension is unknown. In this problem, X represents the width of the cuboid.

Q: Can the volume formula work with any units?

Yes! Whether you use centimeters, inches, meters, etc., the formula $ V = L \times W \times H $ always works. Just make sure all dimensions use the same unit!

Volume Formula with Unknown Dimension

It is known that the volume of the cuboid is 90, the height of the cuboid is 5 and its length is equal to 3

Based on the data, find X

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Use the formula for calculating box volume

00:06 height times length times width

00:11 Substitute appropriate values and solve for side X

00:18 Isolate side X

00:21 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

It is known that the volume of the cuboid is 90, the height of the cuboid is 5 and its length is equal to 3

Based on the data, find X

Step-by-step solution

To solve this problem, let's determine the missing dimension $X$ by applying the formula for the volume of a cuboid:

Step 1: Identify given values: Volume $V = 90$ , Height $H = 5$ , Length $L = 3$ .
Step 2: Use the volume formula: $V = L \times W \times H$ .
Step 3: Substitute the known values: $90 = 3 \times X \times 5$ .
Step 4: Simplify and solve for $X$ . First, calculate $3 \times 5$ , which is $15$ .
Step 5: Rearrange the equation: $90 = 15 \times X$ .
Step 6: Solve for $X$ by dividing both sides by 15: $X = \frac{90}{15}$ .
Step 7: Calculate to find $X = 6$ .

Thus, the missing width $X$ of the cuboid is $6$ .

Final Answer

$6$

Key Points to Remember

Essential concepts to master this topic

Formula: Volume equals length times width times height
Technique: Substitute known values: $90 = 3 \times X \times 5$
Check: Verify: $3 \times 6 \times 5 = 90$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by all three dimensions
Don't just divide 90 by one dimension = wrong answer! Students often calculate 90 ÷ 3 = 30 or 90 ÷ 5 = 18, ignoring that volume needs all three dimensions multiplied together. Always substitute all known values into V = L × W × H first.

Practice Quiz

Test your knowledge with interactive questions

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

FAQ

Everything you need to know about this question

What's the difference between length, width, and height in a cuboid?

Length, width, and height are just the three dimensions of a rectangular box. It doesn't matter which dimension you call which - the volume formula works the same way regardless!

Why do I multiply all three dimensions together?

Volume measures how much space is inside the cuboid. You need to account for all three directions: length × width × height gives you the total cubic units that fit inside.

What if I get the formula backwards?

No problem! Just rearrange it correctly. If you have $V = L \times W \times H$ , then $W = \frac{V}{L \times H}$ . Division undoes multiplication!

How do I know which dimension is X?

Look at the diagram carefully! The X label shows which dimension is unknown. In this problem, X represents the width of the cuboid.

Can the volume formula work with any units?

Yes! Whether you use centimeters, inches, meters, etc., the formula $V = L \times W \times H$ always works. Just make sure all dimensions use the same unit!

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