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valkas [14]
2 years ago
13

Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the area of the sector give

n r = 3 cm and Θ =
π
4
.
Mathematics
2 answers:
Anika [276]2 years ago
8 0
Sector area = (Central Angle (Degrees) / 360) * PI * radius^2
One way to solve this is that an angle of (PI/4) = 45 degrees.
45 degrees is one eighth of a circle.
Area of ENTIRE circle = PI*radius^2 = PI * 3^2 = <span> <span> <span> 28.2743338823  </span> </span> </span> square centimeters
Area of the sector is one eighth of this =  <span> <span> <span> 3.5342917353 </span> </span> </span> <span><span> </span> </span> square centimeters

Maslowich2 years ago
4 0

Answer:

Let l be the length of an ac and r be the radius of the circle.

Use the fact that the length of an arc intercepted by an angle is proportional to the radius

i.e

l \propto r

⇒l = r \theta where, \theta is the angle in radian.

To find the Area of the sector:

Given: r = 3 cm and \theta = \frac{\pi}{4}

\text{Area of the sector A} = \pi r^2 \cdot \frac{\theta}{360^{\circ}}

where, \theta is the angle in degree.

Use conversion:

1 radian = \frac{180}{\pi} degree

then;

\frac{\pi}{4} = \frac{\pi}{4 } \times \frac{180}{\pi} = 45^{\circ}

then;

\theta =45^{\circ} and use \pi = 3.14

Substitute the given values we have;

A= 3.14 \cdot 3^2 \cdot \frac{45}{360}

⇒A = 3.14 \cdot 9 \cdot 0.125

Simplify:

A = 3.5325 square cm

Therefore, the area of the sector is, 3.5325 square cm

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