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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

Find the Area of the Sector Whose Arc Length and Radius Are 8 Cm and 3 Cm Respectively. - Geometry Mathematics 2

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प्रश्न

Find the area of the sector whose arc length and radius are 8 cm and 3 cm respectively.

बेरीज

उत्तर

Length of arc, S = 8 cm

Radius of circle, r = 3 cm

`"S" = rθ ⇒ θ = "S"/r = 8/3`radians

`8/3"radians"=180/pixx8/3=(480/pi)@`

`"Area of the sector "=theta/360xxpir^2=480/(360xxpi)xxpir^2=4/3xx9=12"cm"^2`

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2014-2015 (March) Set B

संबंधित प्रश्‍न

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:

(i) The length of the arc

(ii) Area of the sector formed by the arc

(iii) Area of the segment forced by the corresponding chord

[use Π = 22/7]


A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. [Use π = 3.14 and `sqrt3 = 1.73`]


A car has two wipers which do not overlap. Each wiper has blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades [Use π  = `22/7`]


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In the given figure, A is the center of the circle. ∠ABC = 45° and AC = 7√2 cm. Find the area of segment BXC.


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The radius of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44 cm in length.


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Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by the three animals.


Floor of a room is of dimensions 5 m × 4 m and it is covered with circular tiles of diameters 50 cm each as shown in figure. Find the area of floor that remains uncovered with tiles. (Use π = 3.14)


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In the given figure, arcs have been drawn of radius 7 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.


Find the area of the unshaded region shown in the given figure.


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