Advertisements
Advertisements
प्रश्न
The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius. Express the angle of the sector in degrees, minutes and seconds
Advertisements
उत्तर
Let OAB be the sector of a circle of radius r.
The angle of the sector is θ.
Perimeter of the sector = OA + arc AB + OB arc AB = rθ
∴ Perimeter of the sector = r + r θ + r
= 2r + rθ
= r(2 + θ) ......(1)
Length of the arc of the semi – circle of radius
l = nπ ......(2)
Given that perimeter the circular sector = Length of the arc of the semi circle of radius r
From equations (1) and (2), we have
r(2 + θ) = πr
2 + θ = π
θ = π – 2
θ = `22/7 - 2 = (22 - 14)/7`
θ = `8/7` radians
θ = `(8/7 xx 180/pi)^circ`
= `8/7 xx 180/22 xx 7`
θ = `720/11`
= 65° 27' 16"
APPEARS IN
संबंधित प्रश्न
Express the following angles in radian measure:
30°
Express the following angles in radian measure:
135°
Express the following angles in radian measure:
– 205°
Express the following angles in radian measure:
150°
Express the following angles in radian measure:
330°
Find the degree measure corresponding to the following radian measures
`pi/3`
Find the degree measure corresponding to the following radian measures
`pi/9`
Find the degree measure corresponding to the following radian measures
`(2pi)/5`
Find the degree measure corresponding to the following radian measures
`(7pi)/3`
Find the degree measure corresponding to the following radian measures
`(10pi)/9`
What must be the radius of a circular running path, around which an athlete must run 5 times in order to describe 1 km?
In a circle of diameter 40 cm, a chord is of length 20 cm. Find the length of the minor arc of the chord
What is the length of the arc intercepted by a central angle of measure 41° in a circle of radius 10 ft?
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii
A train is moving on a circular track of 1500 m radius at the rate of 66 km/hr. What angle will it turn in 20 seconds?
A circular metallic plate of radius 8 cm and thickness 6 mm is melted and molded into a pie (a sector of the circle with thickness) of radius 16 cm and thickness 4 mm. Find the angle of the sector.
Choose the correct alternative:
A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?
