Formula for calculating the area of a circular fan

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Round fan image is a special geometric form in plane geometry. The following article would like to introduce to you what the concept of fan -shaped is, the formula for calculating the area of a round fan shape, the circumference of a round fan shape. Please refer.

What is a fan image?

The picture is limited by two radius OA, OB and AB round as shown below, called a circular fan shape.

Fan -shaped

So the fan image is part of the circle limited by two radius and one bow

Formula for calculating fan image area

If S is the fan area, the formula for calculating the area of a circular fan has 2 expressions:

$S = \ frac {\ pi \ cdot r^2 \ cdot n} {360}$ or $S = \ Frac {\ ELL \ CDOT R} {2}$

In there:

S Is the area of a round fan
R is the radius of the circle, as shown in the figure, R = OA = OB
ℓ As the length of the supply, in the picture, ℓ has the length of the supply AB.

The formula for calculating the circumference of the circular fan

The circumference formula of the circular fan shape is determined by the formula:

$C = 2r+\ ELL$

In there:

C A fan -shaped circumference
R Is the radius of the center circle o
ℓ Is the length of the supply

Examples of the area of round fan -shaped, round fan circumference

Lesson 1:

Calculate the area of a round fan when you know, radius R = 5 cm, angle n = 30º.

Prize: Apply the formula to calculate the fan image we have:

$S = \ frac {\ pi.r2} {360} = \ frac {\ pi.52.30} {360} = 6.55 (cm2)$

Lesson 2:

Calculate the area of a round fan when you know the radius R = 7 cm, the length of the supply ℓ = 5 cm.

Prize: Apply the formula to calculate the fan image we have:

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$S = \ Frac {ℓ.R} {2} = \ Frac {5.7} {2} = 17.5 (cm2)$

Lesson 3:

Calculate the circumference of a fan shape with an area of 8 cm2, the supply has a length of 5 cm.

Prize: We have:

$S = \ Frac {ℓ.R} {2} ⇒R = \ Frac {2s} {ℓ} = \ Frac {2.8} {5} = 3.2 (cm)$

Based on the formula of the circumference of the fan shape we have: C = 2R + ℓ = 2.3.2 + 5 = 11.4 (cm).

Also do not miss a series of articles calculating the area of the circle, the area of the pyramid and another series of pictures.

Formula for calculating the area of a circular fan

What is a fan image?

Formula for calculating fan image area

The formula for calculating the circumference of the circular fan