Question

The
diameter of circle is 10 cm. Find
the length of the arc when the correspo-
nding central angle is
45
3) 210 4) 180
(π=3.14)​

Answer 1

GivEn:

• Diameter = 10 cm

To find:

• The length of the arc when the corresponding central angle is 45°?

Solution:

• Let's consider central angle as θ,

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« Now, Finding radius of the circle,

★ Radius = Diameter/2

⇒ 10/2

⇒ 5 cm

∴ Hence, The radius of the circle is 5 cm.

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Now, Let's find length of the arc,

As we know that,

• Length of the arc = θ/360 × 2πr

⇒ 45/360 × 2 × 3.14 × 5

⇒ 45/360 × 31.4

⇒ 0.125 × 31.4

⇒ 3.925

∴ Hence, Length of the arc is 3.925.

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★ More To know:

• Area of Circle = πr²

• TSA of cylinder = 2πr(r + h)

• CSA of cylinder = 2πrh

• Volume of cylinder = πr²h

Answer 2

Given:-

• Diameter of circle = 10 cm

• Corresponding central angle = 45°

To Find:-

• Length of the Arc

Formula Used:-

• ${\boxed{\bf{Radius=\dfrac{Diameter}{2}}}}$

• ${\boxed{\bf{l=\dfrac{θ}{360}\times 2\pi r}}}$

Solution:-

Firstly,

$\sf :\implies\:Radius=\dfrac{Diameter}{2}$

$\sf :\implies\:Radius=\dfrac{10}{2}$

$\sf :\implies\:Radius=5\:cm$

Now Using Formula,

$\sf :\implies\:l=\dfrac{θ}{360}\times 2\pi r$

Here,

• θ = 45°

• r = 5 cm

Putting values,

$\sf :\implies\:l=\dfrac{45}{360}\times 2\times 3.14\times 5$

$\sf :\implies\:l=\dfrac{1}{8}\times 2\times 3.14\times 5$

$\sf :\implies\:l=\dfrac{31.4}{8}$

$\sf :\implies\:l=3.925\:cm$

Hence, The length of the Arc is 3.925 cm.

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