Calculate Surface Area: 3×5×8 Cuboid Problem

Surface Area Calculation with Three-Dimensional Cuboids

Look at the the cuboid below.

What is its surface area?

333555888

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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
00:03 We'll use the formula to calculate the surface area of a box
00:08 2 x (the sum of face areas)
00:16 Substitute appropriate values into the formula and solve to find the surface area
00:43 We'll solve each multiplication separately and add them together
00:59 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 the cuboid below.

What is its surface area?

333555888

2

Step-by-step solution

First, we recall the formula for the surface area of a cuboid:

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

As in the cuboid the opposite faces are equal to each other, the given data is sufficient to arrive at a solution.

We replace the data in the formula:

(8*5+3*5+8*3) *2 =

(40+15+24) *2 =

79*2 =

158

3

Final Answer

158

Key Points to Remember

Essential concepts to master this topic
  • Formula: Surface area = 2(lw + lh + wh) for all faces
  • Technique: Calculate each face area: 3×5=15, 3×8=24, 5×8=40
  • Check: Add face areas (15+24+40)×2 = 79×2 = 158 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to multiply by 2 for opposite faces
    Don't calculate just one of each face type (15+24+40=79) and stop there! This only counts half the cuboid's faces. Always multiply by 2 since each cuboid has 6 faces arranged in 3 pairs of identical opposite faces.

Practice Quiz

Test your knowledge with interactive questions

Identify the correct 2D pattern of the given cuboid:

444444999

FAQ

Everything you need to know about this question

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

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A cuboid has 6 faces total - but they come in 3 pairs of identical opposite faces. The front and back faces are identical, the left and right faces are identical, and the top and bottom faces are identical. So we calculate the area of one face from each pair, then multiply by 2!

How do I remember which dimensions to multiply together?

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Think of the three different face types:

  • Front/back faces: width × height
  • Left/right faces: length × height
  • Top/bottom faces: length × width
Each uses two of the three dimensions.

What if I get the dimensions mixed up?

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Don't worry! As long as you use each dimension exactly twice in your calculations, you'll get the right answer. The formula 2(lw+lh+wh)2(lw + lh + wh) automatically accounts for this.

Can I solve this without the formula?

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Yes! You can visualize each face and calculate them individually:

  • 2 faces of 3×5 = 30
  • 2 faces of 3×8 = 48
  • 2 faces of 5×8 = 80
Then add: 30+48+80 = 158

How do I check if my answer makes sense?

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Your surface area should be larger than any single face area. Here, our biggest face is 5×8=40, and 158>40 ✓. Also, it should be less than if we calculated all faces separately without sharing edges.

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