Find the circumference of a circle

Since early history, mathematicians have known that the ratio of the distance around a circle (the circumference) divided by the length of its diameter is approximately 3.

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Views #: 230

Questions #: 10

Time: 10 minutes

Pass Score: 80.0%

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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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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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Circumference – Exact Answer Using π

2 pts

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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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Circumference – Decimal Approximation

1 pts

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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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Circumference – Exact Answer (r = 12 m)

2 pts

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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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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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Circumference Using the Diameter

2 pts

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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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Find the Radius Then the Circumference

2 pts

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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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Perimeter of a Norman Window (Rectangle + Semicircle)

3 pts

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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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Complete the Circumference Formulas

3 pts

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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

2π

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Year 8

The Definition of Pi (π)

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Explanation

The Two Circumference Formulas

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Explanation

Circumference – Exact Answer Using π

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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)

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Explanation

Complete the Circumference Formulas

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