Calculate Surface Area: 11 cm Cube with Equal Edges

Q: Why do we multiply by 6 in the surface area formula?

A cube has 6 faces - top, bottom, front, back, left, and right. Each face is a square with the same area. So we calculate the area of one square face and multiply by 6 to get the total surface area.

Q: What's the difference between surface area and volume?

Surface area measures the total area of all outer faces (like wrapping paper needed). Volume measures the space inside the cube. For surface area we use $ 6s^2 $, for volume we use $ s^3 $.

Q: Do I need to memorize the formula?

It helps, but you can also think it through! A cube has 6 square faces, each with area $ s^2 $. So total area = $ 6 \times s^2 = 6s^2 $. Understanding beats memorizing!

Q: How can I check if my answer makes sense?

Ask yourself: Is my answer reasonable? Each face is $ 11^2 = 121 $ cm², so 6 faces should be around $ 6 \times 120 = 720 $ cm². Our answer of 726 cm² is very close, so it makes sense!

Surface Area Formula with Cube Geometry

The edges of a cube are 11 cm long.

Calculate the surface area of the cube.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the surface area of the cube

00:03 Edge length according to the given data

00:07 We'll use the formula to calculate the surface area of a cube

00:11 Multiply the number of faces (6) by the area of one face

00:14 Substitute appropriate values and solve to find the surface area

00:23 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

The edges of a cube are 11 cm long.

Calculate the surface area of the cube.

Step-by-step solution

To solve this problem, we will calculate the surface area of the cube with edge length 11 cm using the formula for the surface area of a cube. The steps are as follows:

Step 1: Identify the side length of the cube
The problem states that each edge of the cube is 11 cm long.
Step 2: Apply the formula for the surface area of a cube
The surface area $A$ of a cube is given by the formula $A = 6s^2$ , where $s$ is the side length.
Step 3: Perform the calculation
Substitute $s = 11$ cm into the formula:

$A = 6 \times 11^2$

Calculate $11^2 = 121$ :

$A = 6 \times 121$

Calculate $6 \times 121 = 726$ .

Therefore, the surface area of the cube is $\textbf{726 cm}^2$ .

Looking at the choices provided, the correct answer is the third choice: $726 \text{ cm}^2$ .

Therefore, the solution to the problem is $\textbf{726 cm}^2$ .

Final Answer

$726$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Surface area of cube = $6s^2$ where s is edge length
Calculation: For 11 cm cube: $6 \times 11^2 = 6 \times 121 = 726$ cm²
Check: Cube has 6 faces, each $11^2 = 121$ cm², total = 726 cm² ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 6 for all six faces
Don't just calculate $11^2 = 121$ and think that's the answer! This only gives you the area of one face. A cube has 6 identical square faces. Always multiply the area of one face by 6 to get the total surface area.

Practice Quiz

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Identify the correct 2D pattern of the given cuboid:

FAQ

Everything you need to know about this question

Why do we multiply by 6 in the surface area formula?

A cube has 6 faces - top, bottom, front, back, left, and right. Each face is a square with the same area. So we calculate the area of one square face and multiply by 6 to get the total surface area.

What's the difference between surface area and volume?

Surface area measures the total area of all outer faces (like wrapping paper needed). Volume measures the space inside the cube. For surface area we use $6s^2$ , for volume we use $s^3$ .

Do I need to memorize the formula?

It helps, but you can also think it through! A cube has 6 square faces, each with area $s^2$ . So total area = $6 \times s^2 = 6s^2$ . Understanding beats memorizing!

What if the edge length has decimals?

Use the same formula! Just be careful when squaring decimal numbers. For example, if edge = 2.5 cm, then surface area = $6 \times (2.5)^2 = 6 \times 6.25 = 37.5$ cm².

How can I check if my answer makes sense?

Ask yourself: Is my answer reasonable? Each face is $11^2 = 121$ cm², so 6 faces should be around $6 \times 120 = 720$ cm². Our answer of 726 cm² is very close, so it makes sense!

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