Calculate Surface Area: 3×3×11 Cuboid with Given Dimensions

Surface Area with Opposite Face Pairs

Look at the cuboid below.

What is its surface area?

333333111111

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the surface area of the box
00:04 We'll use the formula to calculate the surface area of a box
00:09 2 x (the sum of face areas)
00:15 Substitute the appropriate values into the formula and solve to find the surface area
00:43 Solve each multiplication separately and add them together
00:57 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the cuboid below.

What is its surface area?

333333111111

2

Step-by-step solution

We identified that the faces are

3*3, 3*11, 11*3
As the opposite faces of an cuboid are equal, we know that for each face we find there is another face, therefore:

3*3, 3*11, 11*3

or

(3*3, 3*11, 11*3 ) *2

To find the surface area, we will have to add up all these areas, therefore:

(3*3+3*11+11*3 )*2

And this is actually the formula for the surface area!

We calculate:

(9+33+33)*2

(75)*2

150

3

Final Answer

150

Key Points to Remember

Essential concepts to master this topic
  • Formula: Surface area equals 2(lw + lh + wh) for cuboids
  • Technique: Calculate one face of each type: 3×3=9, 3×11=33, 3×11=33
  • Check: Count 6 faces total: two 3×3, two 3×11, two 3×11 faces ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to double each face area
    Don't calculate just one of each face type and add them = incomplete answer of 75! This ignores that cuboids have opposite faces. Always multiply by 2 or count all 6 faces individually.

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 I multiply by 2 in the surface area formula?

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Because a cuboid has 6 faces total, but they come in 3 pairs of identical opposite faces. So you calculate one face of each type, then multiply by 2 to count both faces in each pair.

What if two dimensions are the same like 3×3×11?

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You still have 3 different face types! The faces are 3×3, 3×11, and 3×11. Even though two face types have the same area (33), you still need to count both pairs when calculating.

How can I visualize all the faces?

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Imagine unfolding the cuboid like a cardboard box! You'll see:

  • 2 square faces (3×3)
  • 4 rectangular faces (all 3×11)
That's 6 faces total.

Is there a shortcut for this calculation?

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Yes! Use the formula 2(lw+lh+wh) 2(lw + lh + wh) where l=length, w=width, h=height. For this problem: 2(3×3+3×11+3×11)=2(75)=150 2(3×3 + 3×11 + 3×11) = 2(75) = 150

What if I get confused about which faces are which?

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Label the dimensions clearly! If it's 3×3×11, you have length=3, width=3, height=11. The three face types are: top/bottom (3×3), front/back (3×11), and left/right (3×11).

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