Advertisements
Advertisements
Question
In the given figure, OACB is a quadrant of circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the
(i) Quadrant OACB
(ii) Shaded region
[Use Π = 22/7]
Solution
(i) Since OACB is a quadrant, it will subtend 90° angle at O.
Area of quadrant OACB = `90^@/360^@ xx pir^2`
`=1/4xx22/7xx(3.5)^2 = 1/4xx22/7xx(7/2)^2`
`= (11xx7xx7)/(2xx7xx2xx2) = 77/8 cm^2`
(ii) Area of ΔOBD = 1/2 x OB x OD
`= 1/2xx3.5xx2`
`= 1/2xx7/2xx2`
`= 7/2 cm^2`
Area of the shaded region = Area of quadrant OACB − Area of ΔOBD
`= 77/8-7/2`
`= (77-28)/8`
`= 49/8 cm^2`
APPEARS IN
RELATED QUESTIONS
Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre [Use Π = 22/7]
From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in the given figure. Find the area of the remaining portion of the square [Use Π = 22/7]
In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. [Use Π = 22/7]
The radii of two circles are 19cm and 9 cm respectively. Find the radius and area of the circle which has circumferences is equal to sum of circumference of two circles.
Find the area of triangle whose base measures 24 cm and the corresponding height measure 14.5 cm.
Find the area of the triangle whose sides are 18 cm, 24 cm and 30 cm. Also find the height corresponding to the smallest side.
The perimeter of a triangular field is 240m, and its sides are in the ratio 25:17:12. Find the area of the field. Also, find the cost of ploughing the field at ₹ 40 per `m^2`
The difference between the sides at the right angles in a right-angled triangle is 7 cm. the area of the triangle is `60 cm^2` . Find its perimeter.
Find the area of shaded region in Fig. 4, where a circle of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm. (Use π = 3.14 and\[\sqrt{3}\] =1.73)
Read the following passage:
Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a hill, which will have adequate space for parking. After survey, it was decided to build rectangular playground, with a semi-circular area allotted for parking at one end of the playground. The length and breadth of the rectangular playground are 14 units and 7 units, respectively. There are two quadrants of radius 2 units on one side for special seats. |
Based on the above information, answer the following questions:
- What is the total perimeter of the parking area?
- (a) What is the total area of parking and the two quadrants?
OR
(b) What is the ratio of area of playground to the area of parking area? - Find the cost of fencing the playground and parking area at the rate of ₹ 2 per unit.
