Q.4: Find the area of the segment AYB shown in the figure, if the radius of the circle is 21 cm and ∠ AOB = 120°. (Use π = 22/7).
Q.5: Find the area of the shaded design in given figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use π = 3.14).
Q.6: A round table cover has six equal designs as shown in the 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 3 = 1.7)
Answers
Answer:
5)Given:
Side of square ABCD=10cm
Area of square ABCD=(side)
2
=10
2
=100sq.cm
Given semicircle is drawn with side of square as diameter.
So, Diameter of semicircle=Side of square=10cm
Radius of semicircle=
2
side
=
2
10
=5cm
Area of semi-circle AD=
2
1
×Area of circle
=
2
1
×πr
2
=
2
1
×3.14×5
2
=
2
3.14×25
Since radius is same for semi-circle AD,BC,AB,CD
Area of semi circleAD=Area of semi circle BC=Area of semicircle AB
=Area of semicircle CD=
2
3.14×25
Area of 4 semicircles−Area of shaded region=Area of square ABCD
Area of shaded region=Area of 4 semicircles−Area of square ABCD
=4×
2
3.14×25
−100=157−100=57cm
2
Step-by-step explanation:
(I)Area of the segment AYB .
(ii)Let us mark the four unshaded regions as I, II, III and IV (Fig. 12.50). Area of I + Area of III .
(iii) It can be observed that these designs are segments of the circle.
Consider segment APB. Chord AB is a side of the hexagon. Each chord will substitute 360o/6 = 60o at the centre of the circle.
In ΔOAB, ∠OAB = ∠OBA (As OA = OB)
∠AOB = 60°
∠OAB + ∠OBA + ∠AOB = 180°
2∠OAB = 180° − 60° = 120°
∠OAB = 60°
Therefore, ΔOAB is an equilateral triangle.
Area of ΔOAB = = √3/4 x (28)2=196√3 =196 x 1.7=333.2 cm2
Area of sector OAPB = √3/4×side²
= √3/4 x (28)2=196√3 =196 x 1.7=333.2 cm2
Area of sector OAPB = 60/360×πr²
= 1/6 x 22/7 x 28 x 28 =1232/3 cm2
Area of segment APB = Area of sector OAPB − Area of ΔOAB
6× [1232/- 333.2] cm²
=(2464-1999.2)cm2
= 464.8cm2
=Cost of making 1 cm2 designs = Rs 0.35
=Cost of making 464.76 cm2 designs = 464.8 x 0.35 =RS 162.68
Therefore, the cost of making such designs is Rs 162.68.
