Find the circumference of a circle

The Definition of Pi (π)

1 pts

volume_mute

The ratio of the distance around a circle (its circumference \(C\)) to the length of its diameter \(D\) is always the same constant, called pi:

\[\pi = \frac{C}{D} \approx 3.14159265\ldots\]

Which of the following is not a commonly used approximation for π?

\(3.14\)

\(\dfrac{22}{7}\)

\(3.14159265\ldots\)

\(\dfrac{1}{3}\)

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Explanation

The Two Circumference Formulas

1 pts

volume_mute

The circumference of a circle can be calculated using either the diameter \(D\) or the radius \(r\). Study the labeled circle below.

If the radius is known, which formula is used to find the circumference?

\(C = \pi D\)

\(C = 2\pi r\)

\(C = \pi r^2\)

\(C = 4r\)

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Explanation

Circumference – Exact Answer Using π

2 pts

volume_mute

Find the exact circumference of the circle shown. Leave the answer in terms of \(\pi\).

\(5\pi\) cm

\(10\pi\) cm

\(25\pi\) cm

\(2\pi\) cm

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Explanation

Circumference – Decimal Approximation

1 pts

volume_mute

The exact circumference of the circle is \(10\pi\) cm. Using \(\pi \approx 3.14\), what is the approximate circumference?

28.6 cm

31.4 cm

34.2 cm

37.0 cm

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Explanation

Circumference – Exact Answer (r = 12 m)

2 pts

volume_mute

Find the exact circumference of the circle shown. Leave the answer in terms of \(\pi\).

\(12\pi\) m

\(24\pi\) m

\(144\pi\) m

\(6\pi\) m

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Explanation

Circumference – Approximation (r = 12 m)

1 pts

volume_mute

The exact circumference is \(24\pi\) m. Using \(\pi \approx 3.14\), find the approximate circumference.

73.48 m

74.22 m

75.36 m

76.44 m

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Explanation

Circumference Using the Diameter

2 pts

volume_mute

A tire has a diameter of 15 inches. Use the formula \(C = \pi D\) to find its circumference. Give the exact answer and an approximation using \(\pi \approx 3.14\).

Exact: \(15\pi\) in; Approx: \(\approx 47.1\) in

Exact: \(30\pi\) in; Approx: \(\approx 94.2\) in

Exact: \(7.5\pi\) in; Approx: \(\approx 23.55\) in

Exact: \(225\pi\) in; Approx: \(\approx 706.5\) in

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Explanation

Find the Radius Then the Circumference

2 pts

volume_mute

A circle has a diameter of 20 cm. First find the radius, then find the circumference. Give the approximation using \(\pi \approx 3.14\).

C ≈ 31.4 cm

C ≈ 62.8 cm

C ≈ 125.6 cm

C ≈ 314 cm

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Explanation

Perimeter of a Norman Window (Rectangle + Semicircle)

3 pts

volume_mute

A Norman window is formed by placing a semicircular window on top of a rectangular window. Find the total perimeter of the window shown.

28.42 ft

29.42 ft

30.42 ft

31.42 ft

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Explanation

Complete the Circumference Formulas

3 pts

Drag the correct expression into each placeholder.

Formula 1 (using diameter): \(C =\) (1) \(\times D\)

Formula 2 (using radius): \(C =\) (2) \(\times r\)

π is defined as: \( \pi = \dfrac{C}{?} \) (3)

Semicircle perimeter: \(P =\) (4) \(\times \pi D\)

Please drag and drop the selected option in the right place or type it instead

π

2π

D

½

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The Definition of Pi (π)

Correct Answer

Explanation

The Two Circumference Formulas

Correct Answer

Explanation

Circumference – Exact Answer Using π

Correct Answer

Explanation

Circumference – Decimal Approximation

Correct Answer

Explanation

Circumference – Exact Answer (r = 12 m)

Correct Answer

Explanation

Circumference – Approximation (r = 12 m)

Correct Answer

Explanation

Circumference Using the Diameter

Correct Answer

Explanation

Find the Radius Then the Circumference

Correct Answer

Explanation

Perimeter of a Norman Window (Rectangle + Semicircle)

Correct Answer

Explanation

Complete the Circumference Formulas

Correct Answer

Explanation

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