If the circumference of a circle is 31.4 cm, what is the radius? (Use π ≈ 3.14)

If the circumference of a circle is 31.4 cm, what is the radius? (Use π ≈ 3.14)

• A. 5 cm
• B. 10 cm
• C. 15 cm
• D. 20 cm

Answer: (A)

To determine the radius of a circle when the circumference is known, you can use the formula for the circumference, which is given by: C = 2πr where C is the circumference and r is the radius. Given that the circumference is 31.4 cm and using the approximation π ≈ 3.14, the formula can be used as follows: First, you rearrange the formula to solve for the radius: r = C / (2π) Now, substitute the values into the formula: r = 31.4 cm / (2 × 3.14) Calculating the denominator: 2 × 3.14 = 6.28 Now, substitute back into the formula: r = 31.4 cm / 6.28 If you perform this division, you get: r ≈ 5 cm Thus, the radius of the circle is 5 cm. This confirms that the correct answer matches the calculations of circumference using the given π approximation. Using values higher than the true calculation for π or misapplying the formula leads to results that do not correspond to the derived radius, which clarifies the correctness of the answer provided.

To determine the radius of a circle when the circumference is known, you can use the formula for the circumference, which is given by:

C = 2πr

where C is the circumference and r is the radius. Given that the circumference is 31.4 cm and using the approximation π ≈ 3.14, the formula can be used as follows:

First, you rearrange the formula to solve for the radius:

r = C / (2π)

Now, substitute the values into the formula:

r = 31.4 cm / (2 × 3.14)

Calculating the denominator:

2 × 3.14 = 6.28

Now, substitute back into the formula:

r = 31.4 cm / 6.28

If you perform this division, you get:

r ≈ 5 cm

Thus, the radius of the circle is 5 cm. This confirms that the correct answer matches the calculations of circumference using the given π approximation.

Using values higher than the true calculation for π or misapplying the formula leads to results that do not correspond to the derived radius, which clarifies the correctness of the answer provided.