Compare Circle (4cm radius) vs Square (8cm side): Perimeter Challenge

Q: Do I need to use the exact value of π or can I use 3.14?

For this type of problem, π ≈ 3.14 is perfectly fine! Using 3.14 gives us 25.12 cm, which is close enough to compare with the square's 32 cm perimeter.

Q: What if the question asked for area instead of perimeter?

Then you'd use different formulas: Square area = s² and Circle area = πr². For our shapes: Square = 8² = 64 cm², Circle = π(4²) ≈ 50.24 cm². The square would still be larger!

Q: How do I remember which formula to use?

Think about the shape: Squares have 4 equal sides, so perimeter = 4s. Circles go all the way around, so circumference = 2πr (twice the radius times π).

Q: Is there a shortcut to compare without calculating exact values?

Yes! Compare 4s with 2πr directly. Here: 4(8) = 32 versus 2π(4) = 8π. Since 8π ≈ 25.12, we know 32 > 25.12 without detailed calculation.

Perimeter Comparison with Circle-Square Calculations

The radius of a circle is 4 centimeters.

The length of the side of the a is 8 centimeters.

Which shape has a greater perimeter/circumference?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose which shape has a larger perimeter?

00:03 First let's calculate the perimeter of the square

00:10 The perimeter of a square equals the side length multiplied by the number of sides

00:14 Let's substitute the appropriate values according to the given data and solve to find the perimeter

00:20 This is the square's perimeter, now let's calculate the circle's perimeter

00:27 The given radius

00:33 We'll use the formula for calculating circle circumference

00:38 Let's substitute the appropriate values according to the given data and solve to find the perimeter

00:48 Let's use the value of pi and calculate the perimeter

01:02 This is the circle's perimeter, now let's compare it with the square's perimeter

01:10 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The radius of a circle is 4 centimeters.

The length of the side of the a is 8 centimeters.

Which shape has a greater perimeter/circumference?

Step-by-step solution

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

Step 1: Identify the given information.
Step 2: Use formulas to find the perimeter and the circumference.
Step 3: Compare the calculated values.

Let's perform these steps:

Step 1: The given information includes:

Radius of the circle: $r = 4$ cm
Side length of the square: $s = 8$ cm

Step 2: Calculate the perimeter of the square using the formula $P = 4s$ :

$P = 4 \times 8 = 32 \text{ cm}$

Calculate the circumference of the circle using the formula $C = 2\pi r$ :

$C = 2 \times 3.14 \times 4 = 25.12 \text{ cm}$

Step 3: Compare the results:
We have $P = 32 \text{ cm}$ for the square and $C = 25.12 \text{ cm}$ for the circle.

Therefore, the square has a greater perimeter.

Final Answer

The square

Key Points to Remember

Essential concepts to master this topic

Formulas: Square perimeter = 4s, circle circumference = 2πr
Calculate: Square: 4 × 8 = 32 cm, Circle: 2π × 4 ≈ 25.12 cm
Verify: Compare final values: 32 cm > 25.12 cm, so square wins ✓

Common Mistakes

Avoid these frequent errors

Using diameter instead of radius for circle formula
Don't use C = πd when given radius = you'll get 4π ≈ 12.56 cm instead of 8π ≈ 25.12 cm! This makes the circle seem much smaller than it actually is. Always use C = 2πr when given the radius.

Practice Quiz

Test your knowledge with interactive questions

$$ r=2 $$

Calculate the circumference.

FAQ

Everything you need to know about this question

Do I need to use the exact value of π or can I use 3.14?

For this type of problem, π ≈ 3.14 is perfectly fine! Using 3.14 gives us 25.12 cm, which is close enough to compare with the square's 32 cm perimeter.

Why is the square's perimeter larger even though 8 > 4?

Great observation! Even though the square's side (8 cm) is larger than the circle's radius (4 cm), you need to consider the full formulas. The square uses all 4 sides, while the circle's circumference depends on 2π times the radius.

What if the question asked for area instead of perimeter?

Then you'd use different formulas: Square area = s² and Circle area = πr². For our shapes: Square = 8² = 64 cm², Circle = π(4²) ≈ 50.24 cm². The square would still be larger!

How do I remember which formula to use?

Think about the shape: Squares have 4 equal sides, so perimeter = 4s. Circles go all the way around, so circumference = 2πr (twice the radius times π).

Is there a shortcut to compare without calculating exact values?

Yes! Compare 4s with 2πr directly. Here: 4(8) = 32 versus 2π(4) = 8π. Since 8π ≈ 25.12, we know 32 > 25.12 without detailed calculation.

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