Compare Circle (8cm Diameter) vs Square (6.28cm Sides): Perimeter Challenge

Q: Why is the square side length 6.28 cm exactly?

This problem is designed so both shapes have equal perimeters! The value 6.28 is approximately $ 2\pi $, making the square's perimeter $ 4 \times 2\pi = 8\pi $, which equals the circle's circumference.

Q: Should I use 3.14 or the π button on my calculator?

For this problem, using π ≈ 3.14 gives clean numbers that are easier to compare. Both methods work, but 3.14 makes the calculation clearer: 8 × 3.14 = 25.12.

Q: What if I calculated the circle's area instead of circumference?

Area and perimeter are completely different! The question asks about circumference (distance around the circle), not area (space inside). Always read carefully to know what measurement you need.

Q: How can I remember the difference between diameter and radius?

Think of it this way: diameter goes all the way across the circle through the center, while radius goes halfway from center to edge. Diameter = 2 × radius always!

Q: Is it possible for different shapes to have the same perimeter?

Absolutely! Many different shapes can have the same perimeter but different areas. This is a key concept in geometry - perimeter and area are independent measurements.

Perimeter Comparison with Circle-Square Geometry

The diameter of a circle is 8 centimeters.

The sides of a square are 6.28 centimeters long.

Which shape has the larger circumference or perimeter?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Which shape has a larger perimeter?

00:12 Let's calculate the circle's perimeter.

00:15 The circle's diameter is given in the data.

00:19 We'll use the formula: perimeter equals pi times the diameter.

00:25 Substitute the diameter, and solve for the circle's perimeter.

00:34 We'll use three point one four for pi.

00:43 That's the circle's perimeter.

00:48 Now, let's find the square's perimeter.

00:52 The square's side length is provided in the data.

00:56 The square's perimeter is four times the side length.

01:02 Substitute the side length to find the square's perimeter.

01:11 That's the square's perimeter.

01:17 And that's how we solve the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The diameter of a circle is 8 centimeters.

The sides of a square are 6.28 centimeters long.

Which shape has the larger circumference or perimeter?

Step-by-step solution

To solve this problem, we need to find the circumference of the circle and the perimeter of the square, and then compare the two.

Step 1: Calculate the circumference of the circle
Step 2: Calculate the perimeter of the square
Step 3: Compare the results

Let's execute each step:

Step 1: Calculate the circle's circumference.
Given that the diameter $d = 8$ cm, we use the formula for circumference:
$C = \pi d = \pi \times 8$

Assuming $\pi \approx 3.14$ , the circumference is:
$C = 3.14 \times 8 = 25.12 \, \text{cm}$

Step 2: Calculate the square's perimeter.
Given that the side length $s = 6.28$ cm, we use the formula for perimeter:
$P = 4s = 4 \times 6.28$

Calculate the perimeter:
$P = 4 \times 6.28 = 25.12 \, \text{cm}$

Step 3: Compare the results.
Both the circle's circumference and the square's perimeter are $25.12 \, \text{cm}$ .

Therefore, the solution to the problem is Same circumference.

Final Answer

Same circumference

Key Points to Remember

Essential concepts to master this topic

Formulas: Circle uses C = πd, square uses P = 4s
Calculation: π × 8 = 25.12 and 4 × 6.28 = 25.12
Verification: Both shapes give exactly 25.12 cm when calculated correctly ✓

Common Mistakes

Avoid these frequent errors

Using wrong formula for circle circumference
Don't use C = 2πr when given diameter = confusion and wrong answer! Students often forget that diameter = 2r, so they double-count the radius. Always use C = πd directly when diameter is given.

Practice Quiz

Test your knowledge with interactive questions

$$ r=2 $$

Calculate the circumference.

FAQ

Everything you need to know about this question

Why is the square side length 6.28 cm exactly?

This problem is designed so both shapes have equal perimeters! The value 6.28 is approximately $2\pi$ , making the square's perimeter $4 \times 2\pi = 8\pi$ , which equals the circle's circumference.

Should I use 3.14 or the π button on my calculator?

For this problem, using π ≈ 3.14 gives clean numbers that are easier to compare. Both methods work, but 3.14 makes the calculation clearer: 8 × 3.14 = 25.12.

What if I calculated the circle's area instead of circumference?

Area and perimeter are completely different! The question asks about circumference (distance around the circle), not area (space inside). Always read carefully to know what measurement you need.

How can I remember the difference between diameter and radius?

Think of it this way: diameter goes all the way across the circle through the center, while radius goes halfway from center to edge. Diameter = 2 × radius always!

Is it possible for different shapes to have the same perimeter?

Absolutely! Many different shapes can have the same perimeter but different areas. This is a key concept in geometry - perimeter and area are independent measurements.

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