Compare Circle (r=3cm) vs Rectangle (7cm×3cm): Finding Greater Perimeter

Q: What if the circle and rectangle perimeters were exactly equal?

This can happen! If $ 2\pi r $ exactly equals $ 2(l + w) $, then both shapes have the same perimeter. Always calculate both values to be sure.

Q: Why is it called circumference for circles but perimeter for rectangles?

Circumference is the special term for the distance around a circle. Perimeter is the general term for distance around any shape, including rectangles, triangles, and polygons.

Q: Can I use 3 instead of 3.14 for π to make it easier?

Using π ≈ 3 gives a rough estimate, but π ≈ 3.14 is much more accurate. In this problem, using 3 would give 18 cm instead of 18.85 cm - still less than 20, but less precise.

Q: What if I forget the formulas during a test?

Remember the patterns: circles involve π and radius, rectangles involve adding opposite sides. For circles: "2 times π times radius". For rectangles: "2 times (length plus width)".

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Which shape has a larger perimeter?

00:03 We want to calculate the circumference of the circle

00:06 The radius of the circle according to the given data

00:10 We'll use the formula for calculating circle circumference

00:15 We'll substitute the circle's radius according to the given data and solve for the circumference

00:30 We'll substitute the value of pi

00:40 This is the circle's circumference

00:44 Now we want to calculate the perimeter of the rectangle

00:47 The sides of the rectangle according to the given data

00:51 The rectangle's perimeter equals twice the sum of adjacent sides

01:06 We'll substitute appropriate values and solve for the rectangle's perimeter

01:17 This is the rectangle's perimeter

01:22 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

The radius of a circle is 3 cm.

Dimensions of a rectangle are 7 cm by 3 cm.

Which shape has a greater perimeter/circumference?

2

Step-by-step solution

To determine which shape has the greater perimeter or circumference, we begin by calculating each as follows.

Step 1: Calculate the circumference of the circle.
The formula for the circumference $C$ of a circle is $C = 2\pi r$ .
Given the radius $r = 3$ cm, we have:

$C = 2\pi \times 3 = 6\pi \, \text{cm}$

Step 2: Calculate the perimeter of the rectangle.
The formula for the perimeter $P$ of a rectangle is $P = 2(l + w)$ , where $l$ is the length and $w$ is the width.
Given the dimensions $l = 7$ cm and $w = 3$ cm, we have:

$P = 2(7 + 3) = 2 \times 10 = 20 \, \text{cm}$

Step 3: Compare the circumference and the perimeter.
The calculated circumference of the circle is $6\pi \approx 18.85 \, \text{cm}$ (using $\pi \approx 3.1416$ ).
The perimeter of the rectangle is $20 \, \text{cm}$ .

Since $20 \, \text{cm} > 6\pi \, \text{cm} \approx 18.85 \, \text{cm}$ , the rectangle has a greater perimeter than the circumference of the circle.

Therefore, the shape with the greater perimeter/circumference is the rectangle.

3

Final Answer

The rectangle

Key Points to Remember

Essential concepts to master this topic

Formulas: Circle circumference $C = 2\pi r$ , rectangle perimeter $P = 2(l + w)$
Calculation: Circle: $6\pi \approx 18.85$ cm, Rectangle: $2(7+3) = 20$ cm
Compare: Use decimal approximation $\pi \approx 3.14$ to determine 20 > 18.85 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to convert π to decimal for comparison
Don't leave your circle answer as 6π and try to compare directly with 20! You can't easily tell which is bigger without converting. Always use π ≈ 3.14 to get 6π ≈ 18.85, then compare decimal values.

Practice Quiz

Test your knowledge with interactive questions

$$ r=11 $$

Calculate the circumference.

FAQ

Everything you need to know about this question

Do I always need to use π ≈ 3.14 for comparisons?

+

Yes! When comparing a circumference containing π to a regular number, you must convert π to its decimal approximation. Use π ≈ 3.14 or π ≈ 3.1416 for more precision.

What if the circle and rectangle perimeters were exactly equal?

+

This can happen! If $2\pi r$ exactly equals $2(l + w)$ , then both shapes have the same perimeter. Always calculate both values to be sure.

Why is it called circumference for circles but perimeter for rectangles?

+

Circumference is the special term for the distance around a circle. Perimeter is the general term for distance around any shape, including rectangles, triangles, and polygons.

Can I use 3 instead of 3.14 for π to make it easier?

+

Using π ≈ 3 gives a rough estimate, but π ≈ 3.14 is much more accurate. In this problem, using 3 would give 18 cm instead of 18.85 cm - still less than 20, but less precise.

What if I forget the formulas during a test?

+

Remember the patterns: circles involve π and radius, rectangles involve adding opposite sides. For circles: "2 times π times radius". For rectangles: "2 times (length plus width)".

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Compare Circle (r=3cm) vs Rectangle (7cm×3cm): Finding Greater Perimeter

Perimeter Comparison with Circle and Rectangle

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