Calculate Cube Edge Length: Given Face Area of 9 cm²

Q: Why do I take the square root of the face area?

Because each face of a cube is a square, and the area of a square equals $ \text{side}^2 $. To find the side length, we reverse this by taking the square root of the area.

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

Face area is the area of one square face (9 cm²). Surface area is the total area of all 6 faces combined. For this cube, surface area = 6 × 9 = 54 cm².

Q: How do I know √9 equals 3?

Think: what number times itself gives 9? Since $ 3 \times 3 = 9 $, we know $ \sqrt{9} = 3 $. Perfect squares like 9 always have whole number square roots!

Q: Do all cubes have square faces?

Yes! By definition, a cube has 6 identical square faces. If the faces weren't squares, it would be a different type of rectangular prism, not a cube.

Q: What if the face area wasn't a perfect square?

Then the edge length would be an irrational number. For example, if face area = 8 cm², then edge = $ \sqrt{8} \approx 2.83 $ cm. You'd leave it as $ \sqrt{8} $ or use a calculator.

Square Root Applications with Geometric Shapes

Each face of a cube has an area of 9 cm².

How long are the edges 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 cube's diagonal

00:03 Let's mark the cube's edge as A, all edges are equal

00:06 Each face of the cube is a square

00:09 We'll use the formula for calculating square area (side multiplied by side)

00:12 We'll substitute the area value according to the given data and solve for A

00:15 Take the square root

00:24 We'll find the two possibilities for the edge

00:28 A represents the length of an edge so it must be positive

00:33 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

Each face of a cube has an area of 9 cm².

How long are the edges of the cube?

Step-by-step solution

To find the edge length of the cube, we start by noting that:

Each face of the cube is a square with an area of $9 \text{ cm}^2$ .

Let's denote the edge length of the cube as $s$ . Since each face of the cube is a square:

$s^2 = 9$

To find $s$ , we take the square root of both sides:

$s = \sqrt{9}$

$s = 3 \text{ cm}$

Therefore, the length of each edge of the cube is $3$ cm.

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Cube Face Rule: Each face is a square with area = edge²
Square Root Method: If area = 9, then edge = √9 = 3
Verification: Check by squaring: 3² = 9 cm² matches given area ✓

Common Mistakes

Avoid these frequent errors

Confusing face area with total surface area
Don't use 9 cm² as the total surface area of the cube = wrong edge length! A cube has 6 faces, so total surface area would be 54 cm². Always remember that the given 9 cm² is the area of just ONE face.

Practice Quiz

Test your knowledge with interactive questions

A cube has a total of 14 edges.

FAQ

Everything you need to know about this question

Why do I take the square root of the face area?

Because each face of a cube is a square, and the area of a square equals $\text{side}^2$ . To find the side length, we reverse this by taking the square root of the area.

What's the difference between face area and surface area?

Face area is the area of one square face (9 cm²). Surface area is the total area of all 6 faces combined. For this cube, surface area = 6 × 9 = 54 cm².

How do I know √9 equals 3?

Think: what number times itself gives 9? Since $3 \times 3 = 9$ , we know $\sqrt{9} = 3$ . Perfect squares like 9 always have whole number square roots!

Do all cubes have square faces?

Yes! By definition, a cube has 6 identical square faces. If the faces weren't squares, it would be a different type of rectangular prism, not a cube.

What if the face area wasn't a perfect square?

Then the edge length would be an irrational number. For example, if face area = 8 cm², then edge = $\sqrt{8} \approx 2.83$ cm. You'd leave it as $\sqrt{8}$ or use a calculator.

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