Exploring Circumference

Diego measured the diameter and circumference of several circular objects and recorded his measurements in the table. One of his measurements is inaccurate. Which measurement is it? Explain how you know.

• half dollar coin: diameter 3 cm, circumference 10 cm

• flying disc: diameter 23 cm, circumference 28 cm

• jar lid: diameter 8 cm, circumference 25 cm

• flower pot: diameter 15 cm, circumference 48 cm

What is the circumference?

• 48

• 96

• 24

• 18

Answer explanation

The circumference of a circle is calculated using the formula C = 2πr. If the correct answer is 48, it suggests that the radius or diameter used in the calculation leads to this value, confirming 48 as the correct choice.

• 31.4 cm

• 30 cm

• 32 cm

• 28 cm

Answer explanation

To find the circumference of a circle, use the formula C = πd. Here, d = 10 cm. Thus, C = 3.14 * 10 = 31.4 cm. Therefore, the correct answer is 31.4 cm.

• 10 cm

• 20 cm

• 5 cm

• 15 cm

Answer explanation

To find the radius, use the formula for circumference: C = 2πr. Given C = 62.8 cm and π ≈ 3.14, we have 62.8 = 2 × 3.14 × r. Solving for r gives r = 10 cm, which is the correct answer.

• 21.98 cm

• 22 cm

• 21 cm

• 22.98 cm

Answer explanation

To find the circumference of a circle, use the formula C = 2πr. Here, r = 3.5 cm. Thus, C = 2 × 3.14 × 3.5 = 21.98 cm. Therefore, the correct answer is 21.98 cm.

• 36.98 cm

• 21.98 cm

• 28 cm

• 22 cm

Answer explanation

The perimeter of a semicircle is calculated as half the circumference plus the diameter. Circumference = πd = 3.14 * 14 = 43.96 cm. Half is 21.98 cm. Adding the diameter (14 cm) gives 21.98 cm, which is the correct answer.

• 12 cm

• 11 cm

• 10 cm

• 9 cm

Answer explanation

To find the diameter, use the formula: circumference = π × diameter. Rearranging gives diameter = circumference / π. Substituting the values: diameter = 37.68 cm / 3.14 ≈ 12 cm. Thus, the correct answer is 12 cm.

• 20.56 cm

• 18.56 cm

• 19.56 cm

• 21.56 cm

Answer explanation

The perimeter of a quarter circle is given by (1/4) * 2 * π * r + 2 * r. For r = 8 cm, this is (1/4) * 2 * 3.14 * 8 + 2 * 8 = 6.28 + 16 = 22.28 cm. However, we only need the arc length: 6.28 cm + 16 cm = 18.56 cm.

• 15 cm

• 5 cm

• 20 cm

• 10 cm

Answer explanation

To find the radius, use the formula for circumference: C = 2πr. Given C = 31.4 cm and π ≈ 3.14, we have 31.4 = 2 × 3.14 × r. Solving for r gives r = 5 cm, which is the correct answer.