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Circle
O shown below has a radius of 25 inches. To the nearest tenth of an inch, determine the length of the arc,
x, subtended by an angle of 2.2 radians.
Answer: inches

Circle $O$ shown below has a radius of $25$ inches. To the nearest tenth of an inch, determine the length of the arc, $x$ , subtended by an angle of $2$ . $2$ radians. $\newline$ Answer: $\square$ inches

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Circles: word problems

Full solution

Q. Circle

O

shown below has a radius of

25

inches. To the nearest tenth of an inch, determine the length of the arc,

x

, subtended by an angle of

2

.

2

radians.

\newline

Answer:

\square

inches

Identify Formula: Identify the formula to calculate the length of an arc in a circle. $\newline$ The length of an arc $s$ in a circle is given by the formula $s = r\theta$ , where $r$ is the radius of the circle and $\theta$ is the central angle in radians.
Plug Given Values: Plug the given values into the formula to calculate the length of the arc. $\newline$ Given: $r = 25$ inches, $\theta = 2.2$ radians $\newline$ $s = r\theta = 25$ inches $* 2.2$ radians
Perform Multiplication: Perform the multiplication to find the length of the arc. $s = 25$ inches $* 2.2$ radians $= 55$ inches
Correct Multiplication: Step $3$ (Correction): Perform the correct multiplication to find the length of the arc. $s = 25$ inches $* 2.2 = 55$ inches
Round Result: Round the result to the nearest tenth of an inch as requested. $\newline$ The length of the arc, to the nearest tenth, is $55.0$ inches.

More problems from Circles: word problems

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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

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\newline

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

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

d

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

h

meters above the ground?

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1

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13\pi h

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13\pi h^{2}

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

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169\pi h^{2}

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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

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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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m+70

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m+0.7

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1.7m

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The radius of a semicircle is

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\newline

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Question

\newline

A man has bent a circular wire of radius

49\text{cm}

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\newline

A)100\text{cm}

\newline

B)50\text{cm}

\newline

C)98\text{cm}

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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

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Question

The hypotenuse of a right triangle measures

17 \mathrm{~cm}

and one of its legs measures

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

\newline

\square

\mathrm{cm}

Posted 8 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 9 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}

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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 9 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 9 months ago

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