Surface Area of Cuboid = 18X + 7: Find the Unknown Dimension X

Surface Area Formulas with Impossible Conditions

The surface area of the cuboid is 18X + 7.

Calculate X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:03 We'll use the formula for calculating the surface area of a box
00:08 2 multiplied by (sum of face areas)
00:15 We'll substitute appropriate values and solve for X
00:52 We'll solve each multiplication separately and sum
01:06 We'll properly expand brackets, multiply by each factor
01:22 We'll isolate X
01:33 We got an illogical expression, therefore there's no solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The surface area of the cuboid is 18X + 7.

Calculate X.

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2

Step-by-step solution

To determine the value of X X , we'll use the formula for the surface area of a cuboid:

The formula for the surface area of a cuboid is 2(lw+lh+wh) 2(lw + lh + wh) .

Given that l=5 l = 5 , w=4 w = 4 , and h=X h = X , we plug these values into the surface area formula:

2(5×4+5×X+4×X)=2(20+5X+4X)=2(20+9X)=40+18X 2(5 \times 4 + 5 \times X + 4 \times X) = 2(20 + 5X + 4X) = 2(20 + 9X) = 40 + 18X

We equate this expression to the given surface area:

40+18X=18X+7 40 + 18X = 18X + 7

By simplifying, we subtract 18X 18X from both sides:

40=7 40 = 7

Which simplifies to a contradiction, demonstrating that these conditions are not possible with the given figure.

Conclusively, the given surface area is not possible.

3

Final Answer

The given surface area is not possible.

Key Points to Remember

Essential concepts to master this topic
  • Formula: Surface area of cuboid is 2(lw+lh+wh) 2(lw + lh + wh)
  • Technique: Calculate 2(5×4+5X+4X)=40+18X 2(5 \times 4 + 5X + 4X) = 40 + 18X
  • Check: If 40+18X=18X+7 40 + 18X = 18X + 7 gives 40=7 40 = 7 , condition is impossible ✓

Common Mistakes

Avoid these frequent errors
  • Trying to solve the impossible equation algebraically
    Don't keep manipulating 40+18X=18X+7 40 + 18X = 18X + 7 to find X = some number! When you get 40 = 7, this means the original conditions cannot exist in reality. Always recognize when a mathematical contradiction indicates an impossible scenario.

Practice Quiz

Test your knowledge with interactive questions

A cuboid is shown below:

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What is the surface area of the cuboid?

FAQ

Everything you need to know about this question

What does it mean when I get 40 = 7 in my calculation?

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This is a mathematical contradiction! When you simplify and get an impossible statement like 40 = 7, it means the original problem conditions cannot exist in the real world.

How do I know if a surface area problem is impossible?

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Calculate the surface area using the cuboid formula 2(lw+lh+wh) 2(lw + lh + wh) . If this doesn't equal the given expression for any value of the unknown, the problem is impossible.

Should I still try different values of X to see if one works?

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No! Once you've proven mathematically that the equation leads to a contradiction (like 40 = 7), no value of X can make it work. Trust the algebra!

Can real cuboids have impossible surface areas?

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In real life, every cuboid has a specific surface area based on its dimensions. If someone gives you dimensions and a surface area that don't match the formula, it's not a real cuboid.

What should I write as my final answer for impossible problems?

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State clearly: "The given surface area is not possible" or "No solution exists". Don't try to force a numerical answer when the math shows it's impossible.

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