Calculate Cube Edge Length: Given Face Area of 25 cm²

Q: Why is the edge length the square root of the face area?

Each face of a cube is a perfect square. Since Area = side × side = s², we solve for s by taking the square root of both sides: s = √Area.

Q: Do all edges of a cube have the same length?

Yes! A cube has 12 edges and they are all identical in length. That's what makes it a cube - all faces are congruent squares.

Q: How is this different from finding the volume?

Face area uses 2D measurement (length × width), while volume uses 3D measurement (length × width × height). Here we only need the area of one square face.

Q: What if the face area wasn't a perfect square like 25?

You'd still use $ s = \sqrt{A} $, but might get a decimal answer. For example, if area = 20 cm², then s = √20 ≈ 4.47 cm.

Q: Can I work backwards to check my answer?

Absolutely! Square your edge length: $ 5^2 = 25 $ cm². If this matches the given face area, your answer is correct!

Cube Edge Length with Face Area

Shown below is a cube, the faces of which each equal 25 cm².

What are the lengths of 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 edge length of the cube

00:03 Let's mark the edges with A, all edges are equal in the cube:

00:06 Face area (square) equals the product of edges

00:09 Substitute appropriate values according to the given data and solve for the edge

00:12 Extract the root

00:15 Find the two possibilities for the edge

00:18 These are the two possibilities for the edge

00:24 The edge represents a length of a side, therefore must be positive

00:29 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

Shown below is a cube, the faces of which each equal 25 cm².

What are the lengths of the edges of the cube?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the area of one face of the cube.
Step 2: Use the formula for the side length of a square face, $s = \sqrt{A}$ , where $A$ is the area.
Step 3: Calculate the side length.

Now, let's work through each step:

Step 1: The problem states that each face of the cube has an area of 25 cm².

Step 2: Since each face is a square, we use the formula $s = \sqrt{A}$ to find the side length, where $A = 25$ cm².

Step 3: Plugging in the value for $A$ , we get $s = \sqrt{25} = 5$ cm.

Therefore, the length of each edge of the cube is $5$ cm.

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Formula: For square faces, edge length equals square root of area
Calculation: $s = \sqrt{25} = 5$ cm using area formula
Verification: Check by squaring: $5^2 = 25$ cm² matches given area ✓

Common Mistakes

Avoid these frequent errors

Confusing face area with total surface area
Don't use the total surface area formula 6s² = 25 for one face! This gives s = √(25/6) ≈ 2.04 cm which is wrong. The problem states each face equals 25 cm², so always use the single face area formula s = √A.

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 is the edge length the square root of the face area?

Each face of a cube is a perfect square. Since Area = side × side = s², we solve for s by taking the square root of both sides: s = √Area.

Do all edges of a cube have the same length?

Yes! A cube has 12 edges and they are all identical in length. That's what makes it a cube - all faces are congruent squares.

How is this different from finding the volume?

Face area uses 2D measurement (length × width), while volume uses 3D measurement (length × width × height). Here we only need the area of one square face.

What if the face area wasn't a perfect square like 25?

You'd still use $s = \sqrt{A}$ , but might get a decimal answer. For example, if area = 20 cm², then s = √20 ≈ 4.47 cm.

Can I work backwards to check my answer?

Absolutely! Square your edge length: $5^2 = 25$ cm². If this matches the given face area, your answer is correct!

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