Advertisements
Advertisements
प्रश्न
In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Find the
- perimeter
- area of the shaded region.
उत्तर
i . Perimeter of shaded region = Length of the arc APB + Length of the arc ARC + Length of the arc BSD + Length of the arc CQD
`=1/2xx2pi"r"_1 + 1/2xx2pi"r"_2 + 1/2xx2pi"r"_4`
`=1/2xx2pi(7/2) + 1/2xx2pi(7)+1/2xx2pi(7/2)`
`=2pi(7/2)+2pi(7)`
`=2pi(7/2+7)`
`=2xx22/7xx21/2`
= 66 cm
ii . Area of shaded region = Area of the arc ARC + Area of the arc BSD - (Area of the arc APB + Area of the arc CQD)
`=1/2xxpi("r"_1)^2+1/2xxpi("r")^2 - [1/2xxpi("r"_3)^2 + 1/2xxpi("r"_4)^2]`
`=1/2xxpi(7)^2+1/2xxpi(7)^2 - [1/2xxpi(7/2)^2+1/2xxpi(7/2)^2]`
`= pi(7)^2 - pi(7/2)^2`
`=pi(49 - 49/4)`
`=22/7xx147/4`
= 115.5 cm2
APPEARS IN
संबंधित प्रश्न
A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find.
- The total length of the silver wire required.
- The area of each sector of the brooch [Use π = `22/7`]
In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.
ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.
A sector of 56° cut out from a circle contains area of 4.4 cm2. Find the radius of the circle
The radius of a circle with centre O is 7 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of minor and major segments.
In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?
The circumference of a circle is 100 cm. The side of a square inscribed in the circle is ______.
The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?
In figure, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn, then find the area of the shaded region of the figure.
The area of the sector of a circle of radius 12 cm is 60π cm2. The central angle of this sector is ______.
