Surface Area 752 cm²: Find X in Cuboid Dimensions (12cm × 8cm × (X+4))

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

A cuboid has 6 faces arranged in 3 pairs of identical opposite faces. Each pair has the same area: top/bottom = lw, front/back = lh, left/right = wh. So we calculate one face of each pair then multiply by 2!

Q: How do I expand expressions like 12(X+4)?

Use the distributive property: multiply 12 by each term inside the parentheses. So 12(X+4) = 12×X + 12×4 = 12X + 48. Don't forget to distribute to every term!

Q: Can I solve this problem a different way?

Yes! You could expand everything first: $ 752 = 2(96 + 12X + 48 + 8X + 32) $, then combine like terms. The algebraic steps are the same, just in different order.

Q: How do I know which dimension is length, width, or height?

It doesn't matter for surface area! The formula $ SA = 2(lw + lh + wh) $ works regardless of which dimension you call l, w, or h. Just be consistent with your labeling.

Surface Area Formulas with Variable Dimensions

Look at the cuboid in the figure below.

Its surface area 752 cm².

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 We'll substitute appropriate values according to the given data and solve for X

00:27 We'll simplify what we can

00:46 We'll group like terms

00:55 We'll isolate the unknown X

01:09 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the cuboid in the figure below.

Its surface area 752 cm².

Calculate X.

Step-by-step solution

The surface area formula for a cuboid is given by:

$SA = 2(lw + lh + wh)$

Substitute the given dimensions and surface area into this formula:

$752 = 2(12 \times 8 + 12 \times (X + 4) + 8 \times (X + 4))$

First, calculate each product:

$12 \times 8 = 96$
$12 \times (X + 4) = 12X + 48$
$8 \times (X + 4) = 8X + 32$

Substitute these products back into the equation:

$752 = 2(96 + 12X + 48 + 8X + 32)$

Combine like terms inside the parentheses:

$752 = 2(176 + 20X)$

Distribute the 2:

$752 = 352 + 40X$

Isolate $X$ by subtracting 352 from both sides:

$400 = 40X$

Divide by 40:

$X = 10$

Thus, the value of $X$ is 10 cm.

Final Answer

10 cm

Key Points to Remember

Essential concepts to master this topic

Formula: Surface area of cuboid is $SA = 2(lw + lh + wh)$
Technique: Substitute given values: 752 = 2(12×8 + 12(X+4) + 8(X+4))
Check: When X=10, SA = 2(96+168+112) = 752 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 2 in surface area formula
Don't use SA = lw + lh + wh = 376! This counts each face only once instead of twice (opposite faces). Always remember SA = 2(lw + lh + wh) because a cuboid has 6 faces, with 3 pairs of identical opposite faces.

Practice Quiz

Test your knowledge with interactive questions

A cuboid is shown below:

What is the surface area of the cuboid?

FAQ

Everything you need to know about this question

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

A cuboid has 6 faces arranged in 3 pairs of identical opposite faces. Each pair has the same area: top/bottom = lw, front/back = lh, left/right = wh. So we calculate one face of each pair then multiply by 2!

How do I expand expressions like 12(X+4)?

Use the distributive property: multiply 12 by each term inside the parentheses. So 12(X+4) = 12×X + 12×4 = 12X + 48. Don't forget to distribute to every term!

What if I get a negative value for X?

Check your arithmetic! In geometry problems, dimensions must be positive. If you get negative X, you likely made a calculation error. Also verify that X+4 gives a positive length.

Can I solve this problem a different way?

Yes! You could expand everything first: $752 = 2(96 + 12X + 48 + 8X + 32)$ , then combine like terms. The algebraic steps are the same, just in different order.

How do I know which dimension is length, width, or height?

It doesn't matter for surface area! The formula $SA = 2(lw + lh + wh)$ works regardless of which dimension you call l, w, or h. Just be consistent with your labeling.

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Surface Area 752 cm²: Find X in Cuboid Dimensions (12cm × 8cm × (X+4))

Surface Area Formulas with Variable Dimensions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

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

How do I expand expressions like 12(X+4)?

What if I get a negative value for X?

Can I solve this problem a different way?

How do I know which dimension is length, width, or height?

🌟 Unlock Your Math Potential

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