Find X in a Cuboid: Volume 90, Height 5, Depth 3

Volume Formula with Missing Width

Look at the cuboid in the figure:

XXX555333

The volume of the cuboid is equal to 90.

What is the value of X?

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1

Understand the problem

Look at the cuboid in the figure:

XXX555333

The volume of the cuboid is equal to 90.

What is the value of X?

2

Step-by-step solution

To find the value of X X , we begin by using the formula for the volume of a cuboid, which is given by V=height×depth×width V = \text{height} \times \text{depth} \times \text{width} .

In this problem, the volume V V is 90 cubic units, the height is 5 units, and the depth is 3 units. We need to find the width X X . So, we write the equation:

90=5×3×X 90 = 5 \times 3 \times X

Simplify the equation:

90=15×X 90 = 15 \times X

To solve for X X , divide both sides of the equation by 15:

X=9015 X = \frac{90}{15}

Calculating the right-hand side, we find:

X=6 X = 6

Thus, the width of the cuboid, X X , is 6 units.

The correct answer to the multiple-choice question is choice 4: 6.

3

Final Answer

6

Key Points to Remember

Essential concepts to master this topic
  • Volume Formula: Volume = length × width × height for all cuboids
  • Technique: Substitute known values: 90 = X × 5 × 3 = 15X
  • Check: Verify solution: 6 × 5 × 3 = 90 cubic units ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the dimensions and their labels
    Don't assume X is always height or depth = wrong setup! Students often mix up which dimension corresponds to which measurement. Always identify what X represents by looking at the diagram labels carefully.

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.

121212888555

FAQ

Everything you need to know about this question

How do I know which dimension X represents?

+

Look at the diagram carefully! The labels show that 5 is the height (vertical), 3 is the depth, and X is the width (horizontal base). The positioning of the labels tells you which dimension is which.

Why do we multiply all three dimensions?

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Volume measures 3D space inside the cuboid. You need length × width × height because you're finding how many unit cubes fit in all three directions at once.

What if I get a decimal answer?

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That's fine! Some cuboid problems have decimal solutions. Just make sure your calculation is correct: X=9015=6 X = \frac{90}{15} = 6 gives us a whole number here.

Can I use different formulas for volume?

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No - for cuboids (rectangular prisms), the formula is always Volume = length × width × height. Don't confuse it with formulas for other shapes like cylinders or spheres.

How do I check my work?

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Substitute your answer back: 6×5×3=90 6 \times 5 \times 3 = 90 . If this equals the given volume, your answer is correct!

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