Calculate Cuboid Width: Surface Area 122 cm² with Given Dimensions

Surface Area Formulas with Unknown Dimensions

Look at the cuboid of the figure.

Its surface area is 122 cm².

What is the width of the cuboid?

333777

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the width of the box (W)
00:03 We will use the formula for calculating the surface area of a box
00:11 We will substitute appropriate values and solve for width W
00:24 We will divide by 2
00:36 We will isolate width W
00:50 This is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the cuboid of the figure.

Its surface area is 122 cm².

What is the width of the cuboid?

333777

2

Step-by-step solution

To solve the problem, let's recall the formula for calculating the surface area of a cube:

(width*length + height*width + height*length) *2

Let's substitute the known values into the formula, labelling the missing side X:

2*(3*7+7*X+3*X) = 122

2*(21+7x+3x) = 122

2(21+10x) = 122

Let's now expand the parentheses:

42+20x=122

Now we move terms:

20x=122-42

20x=80

Finally, simplify:

x=4

And that's the solution!

3

Final Answer

4 cm

Key Points to Remember

Essential concepts to master this topic
  • Formula: Surface area of cuboid = 2(lw + lh + wh)
  • Technique: Substitute known values: 2(7×3 + 7×w + 3×w) = 122
  • Check: Verify w=4: 2(21 + 28 + 12) = 2(61) = 122 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to multiply by 2 in surface area formula
    Don't use (lw + lh + wh) = 122 without the factor of 2! This gives wrong answers because cuboids have 6 faces with opposite faces identical. Always remember surface area = 2(lw + lh + wh) for the complete formula.

Practice Quiz

Test your knowledge with interactive questions

A cuboid is shown below:

222333555

What is the surface area of the cuboid?

FAQ

Everything you need to know about this question

Why do we multiply by 2 in the surface area formula?

+

A cuboid has 6 faces that come in 3 pairs of identical rectangles. Each pair contributes the same area twice, so we calculate lw + lh + wh (one of each type) then multiply by 2!

How do I know which dimension is missing from the diagram?

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Look carefully at the labels! In this problem, we can see dimensions 3 cm and 7 cm are given, so the unlabeled dimension is what we need to find.

What if I get a negative answer for the width?

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Check your algebra! Dimensions must be positive since they represent real measurements. A negative result means there's an error in your calculation.

Can I solve this by guessing and checking?

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While possible, it's inefficient! Using algebraic methods with the surface area formula is faster and more reliable than trial and error.

How do I expand 2(21 + 10x) correctly?

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Distribute the 2 to both terms inside: 2(21) + 2(10x) = 42 + 20x. Don't forget to multiply 2 by every term in the parentheses!

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