Find the area of a circle whose circumference measures 100 cm.

Area (to the nearest square centimeter) = cm2

I plugged in everything C = 2 r
C=2x3.14x100= 628 <<< The computer said it was WRONG !
Then, I tried C= 2X3.14X50= 314 !!!

If I am wrong can you EXPLAIN to me what I am doing wrong.

C = 2πr

r = C/2π

area = πr^2 = π(C/2π)^2 = C^2/4π

so, area = 10000/4π = 2500/π = 796 cm^2

Well, it seems like you're on the right track! However, it seems like you're using the formula for the circumference of a circle instead of the formula for the area of a circle. The formula you want to use is:

Area = πr^2

In this formula, π (pi) is approximately 3.14 and r represents the radius of the circle. And since you're given the circumference, you can find the radius using the formula:

Circumference = 2πr

So, if the circumference is 100 cm, you can solve for the radius:

100 cm = 2πr
Divide both sides by 2π:
r = 100 cm / (2π)
r ≈ 15.92 cm (to four decimal places)

Now that you have the radius, you can plug it into the formula for the area:

Area ≈ 3.14 × (15.92 cm)^2
Area ≈ 3.14 × 253.43 cm^2
Area ≈ 796.53 cm^2

So, the area of the circle (to the nearest square centimeter) is approximately 796 cm^2.

You are on the right track, but you made a small mistake in your calculations.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle. In this case, you have already calculated the circumference as 100 cm.

To find the radius, you need to rearrange the formula and solve for the radius:

C = 2πr
100 = 2πr
r = 100 / (2π)
r ≈ 15.92 cm (rounded to two decimal places)

Now that you have the radius, you can use the formula for the area of a circle, which is A = πr^2:

A = π(15.92)^2
A ≈ 795.77 cm^2 (rounded to the nearest square centimeter)

Therefore, the area of the circle, to the nearest square centimeter, is approximately 795 cm^2.

To find the area of a circle given its circumference, you need to use the formula:

C = 2πr

Where C is the circumference and r is the radius of the circle.

In your first attempt, you correctly calculated the circumference using the formula C = 2πr. However, your calculation seems to be incorrect. Let's go through the correct steps.

Given: C = 100 cm

Step 1: Rearrange the formula to solve for r:

C = 2πr
Divide both sides by 2π:
C / (2π) = r

Step 2: Substitute the given value of C into the equation:

r = 100 / (2π)
r ≈ 15.92 cm (rounded to two decimal places)

Step 3: Now that we have the radius, we can find the area of the circle using the formula:

A = πr²

Substituting the value of r we found:

A ≈ 3.14 * (15.92)²
A ≈ 3.14 * 253.44
A ≈ 796.99 cm² (rounded to the nearest square centimeter)

Therefore, the area of the circle, rounded to the nearest square centimeter, is approximately 797 cm².

Please note that your second attempt, C = 2πr = 2 * 3.14 * 50 = 314 cm, gives you the circumference of a circle with a radius of 50 cm. This will not allow you to accurately calculate the area of the circle that has a circumference of 100 cm.