Question

Find the arc length of the partial circle. either enter an exact term in terms of π or use 3.14 for π and enter your answer as a decimal

Answer 1

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Radius = 8 cm

Theta = 90°

Length of arc = Theta/360° × 2πr

=> 90°/360° × 2 × 3.14 × 8

=> 1/4 × 2 × 3.14 × 8

=> 50.24/4

=> 12.56 cm

Answer 2

Step-by-step explanation:

Given :-

Radius of the circle is 8 units

To find :-

Find the length of the arc ?

Solution:-

Radius of the given circle = 8 units

Angle subtended by the arc at the centre =90°

The length of the arc is "l" units ,the radius "r" units and the angle subtended by the arc at the centre is "X° " is (X°/360°)×2πr units

We have r = 8 units X°=90°

π=3.14

On Substituting the values in the above formula

=>l= (90°/360°)×2×π×8 units

=>l=(1/4)×2×π×8

=>l=(2×π×8)/4

=>l=16π/4

=>l=4π units

(or)

=>l=4×3.14

=>l=12.56 units

(or)

Radius (r)=8 units

Angle (X°)=90°

Given figure is the 1/4th of the circle

so length of the arc is the 1/4 th of the Circumference of the circle

=>(1/4)×2πr

=>2πr/4

=>πr/2

Length of the given arc = πr/2 units

=>l=π×8/2

=>l= 4πunits

(or)

=>l=4×3.14 units

=>l=12.56 units

Answer:-

The arc length of the given partial circle is 4π units or 12.56 units

Used formulae:-

• The length of the arc is "l" units ,the radius "r" units and the angle subtended by the arc at the centre is "X° " is (X°/360°)×2πr units

• Circumference of the circle = 2πr units

• π=3.14