Advertisements
Advertisements
प्रश्न
A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48 cm. Find the angle in degrees which is subtended at the centre of hoop.
Advertisements
उत्तर
Given that circular wire is of radius 3 cm
So when it is cut then its length = 2π × 3 = 6π cm.
Again, it is being placed along a circular hoop of radius 48 cm.
Here, s = 6π cm is the length of arc and r = 48 cm is the radius of the circle.
Therefore, the angle θ, in radian, subtended by the arc at the centre of the circle is given by
θ = `"Arc"/"Radius"`
= `(6pi)/48`
= `pi/8`
= 22.5°.
APPEARS IN
संबंधित प्रश्न
Find the radian measure corresponding to the following degree measure:
25°
Find the radian measure corresponding to the following degree measure:
– 47° 30'
Find the radian measure corresponding to the following degree measure:
240°
Find the degree measure corresponding to the following radian measure (Use `pi = 22/7`)
-4
Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)
`(5pi)/3`
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
10 cm
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
15 cm
Find the degree measure corresponding to the following radian measure:
\[\left( \frac{18\pi}{5} \right)\]
Find the degree measure corresponding to the following radian measure:
(−3)c
Find the degree measure corresponding to the following radian measure:
11c
Find the radian measure corresponding to the following degree measure: 135°
Find the radian measure corresponding to the following degree measure: −300°
Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.
Find the magnitude, in radians and degrees, of the interior angle of a regular heptagon.
The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.
The number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9°. Find the number of sides of the polygons.
A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 metres?
A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?
A railway train is travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?
Find the distance from the eye at which a coin of 2 cm diameter should be held so as to conceal the full moon whose angular diameter is 31'.
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm.
If the angles of a triangle are in A.P., then the measures of one of the angles in radians is
The angle between the minute and hour hands of a clock at 8:30 is
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, than the ratio of the radii of the circles is
A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
The radius of the circle whose arc of length 15 π cm makes an angle of \[\frac{3\pi}{4}\] radian at the centre is
Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`
If tan θ = `(-4)/3`, then sin θ is ______.
State whether the statement is True or False? Also give justification.
The equality sinA + sin2A + sin3A = 3 holds for some real value of A.
State whether the statement is True or False? Also give justification.
Sin10° is greater than cos10°
State whether the statement is True or False? Also give justification.
One value of θ which satisfies the equation sin4θ - 2sin2θ - 1 lies between 0 and 2π.
