Question

1. find the arc length of each quarter circle, round to one decimal place.

a) 11m

b) 8.2cm

c) 154mm

Explanation:

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Problem 3: Semicircle Arc Lengths

The arc length of a semicircle is half the circumference of a full circle, given by $L = \frac{1}{2} \times 2\pi r = \pi r$, where $r$ is the radius. For a diameter $d$, $r = \frac{d}{2}$, so $L = \frac{\pi d}{2}$.

Step1: Arc length for semicircle a)

Diameter $d=12$ cm, use $L=\frac{\pi d}{2}$
$L = \frac{\pi \times 12}{2} = 6\pi \approx 18.8$ cm

Step2: Arc length for semicircle b)

Diameter $d=130$ mm, use $L=\frac{\pi d}{2}$
$L = \frac{\pi \times 130}{2} = 65\pi \approx 204.2$ mm

Step3: Arc length for semicircle c)

Radius $r=9$ m, use $L=\pi r$
$L = \pi \times 9 = 9\pi \approx 28.3$ m

Step4: Arc length for semicircle d)

Radius $r=2.55$ m, use $L=\pi r$
$L = \pi \times 2.55 \approx 8.0$ m
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Problem 4: Quarter Circle Arc Lengths

The arc length of a quarter circle is $\frac{1}{4}$ the circumference of a full circle, given by $L = \frac{1}{4} \times 2\pi r = \frac{\pi r}{2}$, where $r$ is the radius.

Step5: Arc length for quarter circle a)

Radius $r=11$ m, use $L=\frac{\pi r}{2}$
$L = \frac{\pi \times 11}{2} = 5.5\pi \approx 17.3$ m

Step6: Arc length for quarter circle b)

Radius $r=8.2$ cm, use $L=\frac{\pi r}{2}$
$L = \frac{\pi \times 8.2}{2} = 4.1\pi \approx 12.9$ cm

Step7: Arc length for quarter circle c)

Radius $r=154$ mm, use $L=\frac{\pi r}{2}$
$L = \frac{\pi \times 154}{2} = 77\pi \approx 241.9$ mm
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Answer:

Problem 3:

a) $18.8$ cm
b) $204.2$ mm
c) $28.3$ m
d) $8.0$ m

Problem 4:

a) $17.3$ m
b) $12.9$ cm
c) $241.9$ mm