Calculate Surface Area of a 2×3×5 Cuboid: Geometric Problem Solving

Surface Area with Rectangular Face Pairs

A cuboid is shown below:

222333555

What is the surface area of the cuboid?

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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 Calculate the surface area of the box
00:11 We'll substitute appropriate values and solve to find the surface area
01:02 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

A cuboid is shown below:

222333555

What is the surface area of the cuboid?

2

Step-by-step solution

Remember that the formula for the surface area of a cuboid is:

(length X width + length X height + width X height) 2

We input the known data into the formula:

2*(3*2+2*5+3*5)

2*(6+10+15)

2*31 = 62

3

Final Answer

62

Key Points to Remember

Essential concepts to master this topic
  • Formula: Surface area = 2(lw + lh + wh) for all six faces
  • Technique: Calculate three different rectangles: 3×2=6, 2×5=10, 3×5=15
  • Check: Six faces total: two of each rectangle type gives 2(6+10+15)=62 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to multiply by 2 for opposite faces
    Don't calculate just one of each face type (3×2 + 2×5 + 3×5 = 31) = missing half the surface! A cuboid has six faces with three pairs of identical opposite faces. Always multiply the sum by 2 to count all faces.

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 need to multiply by 2 at the end?

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A cuboid has six faces that come in three pairs of identical rectangles. Each pair has the same dimensions, so we calculate one of each type (front/back, left/right, top/bottom) then multiply by 2!

How do I identify which faces to calculate?

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Look at the three dimensions: length×width, length×height, and width×height. These give you the three different rectangle types that make up the six faces of your cuboid.

What if I get confused about which dimension is which?

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It doesn't matter! Just make sure you use each dimension exactly twice in your three calculations. For a 2×3×5 cuboid: 2×3, 2×5, and 3×5 covers all combinations.

Can I calculate each face individually instead?

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Yes, but it's more work! You'd calculate six separate rectangles and add them up. The formula method is faster: find the three unique face areas, add them, then double the result.

How do I check if my surface area is reasonable?

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Compare to the volume! For this 2×3×5 cuboid, volume = 30. Surface area should be larger than volume for small cuboids. Our answer of 62 makes sense!

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