Calculate Surface Area: 8×3×1 Cuboid from Net Diagram

Surface Area Calculation with Net Diagrams

An unfolded cuboid is shown below.

What is the surface area of the cuboid?

888111333

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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
00:07 2 x (sum of face areas)
00:16 Substitute appropriate values into the formula and solve for the surface area
00:44 Solve each multiplication separately and add them together
01:03 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

An unfolded cuboid is shown below.

What is the surface area of the cuboid?

888111333

2

Step-by-step solution

To calculate the surface area of the rectangular prism, we will need to identify its three faces (each face appears twice):

1*3

1*8

3*8

 

The formula for the surface area of a rectangular prism is the sum of all the areas of the faces, that is:

We replace the data in the formula:

2*(1*3+1*8+3*8)=
2*(3+8+24) = 
2*35 = 

70

And this is the solution!

3

Final Answer

70

Key Points to Remember

Essential concepts to master this topic
  • Formula: Surface area equals 2(lw + lh + wh) for rectangular prisms
  • Technique: Find three unique faces: 1×3=3, 1×8=8, 3×8=24 square units
  • Check: Total faces should be 6, verify 2(3+8+24)=70 square units ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to double each face area
    Don't calculate just one of each face type (3+8+24=35) = missing half the surface! Each rectangular face appears twice on opposite sides of the cuboid. Always multiply by 2: 2(3+8+24)=70.

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 every rectangular prism has 6 faces, but only 3 different sizes! Each face appears twice - on opposite sides. So you calculate the area of each unique face once, then multiply by 2.

How do I identify the three different face dimensions?

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Look at the three measurements of your cuboid (8, 3, 1). The three faces are formed by pairing these: 8×3, 8×1, and 3×1. Each pair creates one type of rectangular face.

What if I can't see all the faces in the net diagram?

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The net shows all 6 faces unfolded! Count them carefully - you should see exactly 6 rectangles. The dimensions on the edges tell you the length and width of each face.

Can I just add up all the individual face areas I see?

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Yes! That's actually another correct method. Count all 6 rectangles in the net, find each area, then add them up. You'll get the same answer: 70 square units.

Why is my answer different from the given choices?

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Check that you're calculating area (square units), not perimeter or volume. Make sure you've found all three face types and doubled each one. Common wrong answers like 35 come from forgetting to double.

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