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The length of arc
EF is
5pi in. Find the length of the radius.
Radius:
qquad

$3$ . The length of arc $E F$ is $5 \pi$ in. Find the length of the radius. $\newline$ Radius: $\qquad$

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Circles: word problems

Full solution

Q.

3

. The length of arc

E F

is

5 \pi

in. Find the length of the radius.

\newline

Radius:

\qquad

Understand Arc Length Formula: We know the formula for the length of an arc is $L = r\theta$ , where $L$ is the arc length, $r$ is the radius, and $\theta$ is the central angle in radians. $\newline$ Since the arc length $L$ is given as $5\pi$ inches and we're dealing with a circle, the central angle $\theta$ for the full circle is $2\pi$ radians.
Calculate Radius Formula: To find the radius, we rearrange the formula to solve for $r$ : $r = \frac{L}{\theta}$ .
Substitute Values: We plug in the values: $r = \frac{5\pi}{2\pi}$ .
Simplify Equation: Simplify the equation: $r = \frac{5\pi}{2\pi} = \frac{5}{2}$ .
Final Radius Calculation: So, the radius is $\frac{5}{2}$ inches, which is $2$ . $5$ inches.

More problems from Circles: word problems

Question

Skyler climbs a watchtower to guard against forest fires.

\newline

R(h)=\sqrt{13h}

gives the distance, in kilometers, that Skyler can see when their eyes are

h

meters above the ground.

\newline

A(d)=\pi d^{2}

gives the area, in square kilometers, that Skyler can guard when they can see a distance of

d

\newline

Which expression models the area Skyler can guard when their eyes are

h

meters above the ground?

\newline

1

\newline

13\pi h

\newline

13\pi h^{2}

\newline

\sqrt{13\pi h^{2}}

\newline

169\pi h^{2}

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Question

After the outbreak of a mysterious disease, the average wait time at a hospital increased by

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. Before the outbreak, the average wait time at the hospital was

m

\newline

Which of the following expressions could represent the average wait time at the hospital after the outbreak?

\newline

2

\newline

0.7m

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\frac{170}{100}m

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m+70

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m+0.7

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1.7m

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Question

The radius of a semicircle is

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\newline

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

Posted 2 months ago

Question

\newline

A man has bent a circular wire of radius

49\text{cm}

to form a square. Find the sides of a square.

\newline

A)100\text{cm}

\newline

B)50\text{cm}

\newline

C)98\text{cm}

Posted 2 months ago

Question

A quarter is worth

\$0.25

and a half dollar is worth

\$0.50

\newline

a. A quarter has a diameter of

\frac{15}{16}

inch and a height of

\frac{1}{16}

inch. Find the surface area of a quarter. Round your answer to the nearest hundredth.

\newline

b. A half dollar has a diameter of

\frac{9}{8}

inches and a height of

\frac{3}{32}

inch. Find the surface area of a half dollar. Round your answer to the nearest hundredth.

Posted 2 months ago

Question

The hypotenuse of a right triangle measures

17 \mathrm{~cm}

and one of its legs measures

8 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 2 months ago

Question

One of the legs of a right triangle measures

15 \mathrm{~cm}

and its hypotenuse measures

17 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 2 months ago

Question

One of the legs of a right triangle measures

8 \mathrm{~cm}

and the other leg measures

15 \mathrm{~cm}

. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 2 months ago

Question

Find the volume of a right circular cone that has a height of

7.4 \mathrm{~cm}

and a base with a radius of

8.1 \mathrm{~cm}

. Round your answer to the nearest tenth of a cubic centimeter.

\newline

\mathrm{cm}^{3}

Posted 2 months ago

Question

Find the volume of a right circular cone that has a height of

13.3 \mathrm{ft}

and a base with a diameter of

9.4 \mathrm{ft}

. Round your answer to the nearest tenth of a cubic foot.

\newline

\mathrm{ft}^{3}

Posted 2 months ago