Mathematics, 02.08.2019 19:30 QueenB2311

What is the length of an arc on a circle of radius 30.0 cm when θ=60∘?

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Answer from: babbity2009

31.4 cm

Step-by-step explanation:

The length of arc on a circle with radius r and angle $\theta$ (degrees) is given by :-

$l=\frac{\theta}{360^{\circ}}\times(2\pi r)$

Then, the length of an arc on a circle of radius 30.0 cm when $\theta=60^{\circ}$ is given by :-

$l=\frac{60^{\circ}}{360^{\circ}}\times(2\pi (30))\\\\\Rightarrow l=\frac{1}{6}(2(3.14)(30))\\\\\Rightarrow l=31.4\ \text{cm}$

The length of an arc on a circle of radius 30.0 cm when $\theta=60^{\circ}$ is 31.4 cm.

Answer from: Nicolas9979

The length of an arc = 31.4 cm

Further explanation

Circles are two-dimensional builds which are sets of equidistant points at a point called the center point

The distance of these points to the center is called the radius of the circle. While the circle field is an area which is bounded by a circle

There are terms - terms commonly used in circles:

1. The center point2. Radius3. Arc4. Circumference5. Segment6. Chord7. Annulus8. Diameter9. Disc10. Lens

An arc is part of the circumference of a circle

The length of the arc is the distance from the 2 points (arcs) located around the circle

The length of the arc corresponds to the center angle of the circle.

Calculation of the length of the arc can be done in 2 ways, taking into unit of angle, which is expressed in degrees or radians

1. the angle in degree

Formula used

$\large{\boxed{\bold{L=2\pi.r (\frac{\theta}{360})}}}$

2. the angle in radians

Formula used

$\large{\boxed{\bold{L=r.\theta}}}$

1 radians = $\frac{180}{\pi }$ = 57.32°

We just use the first formula because in the taskr , the angle it is known in degrees

r = 30 cm

θ = 60°

L = 2.π.r (θ / 360)

L = 2.3.14.30 (60/360)

L = 31.4 cm

Learn more

circumference

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chord, diameter, secant

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segment division

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Keywords: angle, radians, arcs, central angles, circles, degrees, circumference

What is the length of an arc on a circle of radius 30.0 cm when θ=60∘?

Answer from: Quest

europa2433

step-by-step explanation:

Answer from: Quest

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

= (6 × 4) + (6 × 0.3)

= 24 + 1.8

6 × 4.3 = 25.8

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