Question

73.
Calculate the area of a sector whose diameter and arc length are 30cm and 26cm
respectively
(A)
(B) 175 sq.cm
(C)
(D) 185 sq.cm
195 sq.cm
165 sq.cm
விட்டம் 30 செ.மீ, வில்லின் நீளம் 26 செ.மீ கொண்டுள்ள வட்ட கோணப் பகுதியின் பரப்பு காண்க,
(A) 195 ச.செ.மீ
(B) 175 ச.செ.மீ
(C) 165 ச.செ.மீ
(D) 185 ச.செ.மீ
GSASO/2020​

Answer 1

Answer:

l =ô/360 * 2πr

26 = ô/360 * 2(3.14)(15)

ô = 26 * 360/2(3.14)(15)

ô = 99.3630

A = ô/360 * πr²

= 99.3630/360 *(3.14)(15)²

= 195cm²

Answer 2

Answer:

According to the given information, the area of sector is 195 $cm^2$.

Step-by-step explanation:

• The region of a disc enclosed by two radii and an arc is called a circular sector, also known as a circle sector or disc sector.
• The smaller area is referred to as the minor sector, and the larger area as the major sector.

For the given solution, we have been given the following information :

Diameter (d) = 30cm

Therefore, radius = 15cm

Arc length = 26cm

To find :

Area of the sector

Solution :

• We know that through the following, length of an arc of the circle is given by = θ/360 * 2πR  

• Furthermore, where θ=Angle subtended by an arc at the centre of the circle, measured in degrees.

Therefore, substituting the values we have in the above formula, we get :

26 = θ/360 * 2(3.14)(15)

θ = 26 * 360/2(3.14)(15)

θ = 99.3630

After calculating θ, we will now calculate the area by the formula

A = θ/ 360 * πr^2

Hence, A =  $99.3630 /360$ * $(3.14) (15)^2$

A= $195 cm^2$

Hence the area of the sector is calculated to be $195 cm^2$

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