Advertisements
Advertisements
प्रश्न
Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.
उत्तर
Let the central angle of the sector be θ.
Given that, radius of the sector of a circle (r) = 5 cm
And arc length `(l)` = 3.5 cm
∴ Central angle of the sector,
θ = `("arc length" (l))/"radius"`
⇒ θ = `3.5/5` = 0.7R ...`[∵ θ = l/"r"]`
⇒ θ = `(0.7 xx 180/pi)^circ` ...`[∵ 1"R" = 180^circ/pi "D"^circ]`
Now, area of sector with angle θ = 0.7
= `(pi"r"^2)/360^circ xx (0.7) xx 180^circ/pi`
= `(5)^2/2 xx 0.7`
= `(25 xx 7)/(2 xx 10)`
= `175/20`
= 8.75 cm2
Hence, the required area of the sector of a circle is 8.75 cm2.
APPEARS IN
संबंधित प्रश्न
An umbrella has 8 ribs which are equally spaced. Assuming umbrella to be a flat circle of radius 45 cm. Find the area between the two consecutive ribs of the umbrella.
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. [Use `pi = 22/7`]
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`]
A round table cover has six equal designs, as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs.0.35 per cm2. [Use `sqrt3 = 1.7`]
In the given figure, O is the centre of the circle. m ( arc PQR) = 60° OP = 10 cm. Find the area of the shaded region.( \[\pi\]= 3.14, \[\sqrt{3}\]= 1.73)
Area of a sector of central angle 200° of a circle is 770 cm2. Find the length of the corresponding arc of this sector.
If `theta` is the angle in degrees of a sector of a circle of radius V, then area of the sector is ____________.
The circumference of a circle is 100 cm. The side of a square inscribed in the circle is ______.
With vertices A, B and C of ΔABC as centres, arcs are drawn with radii 14 cm and the three portions of the triangle so obtained are removed. Find the total area removed from the triangle.
