15. In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region. Solution: Radius of the quadrant ABC of circle = 14 cm AB = AC = 14 cm BC is diameter of semicircle. ABC is … Continue reading 15. In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.
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13. In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)
13. In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14) Solution: Side of square = OA = AB = 20 cm Radius of the quadrant = OB OAB is right angled triangle By Pythagoras theorem in … Continue reading 13. In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)
12. In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the(i) quadrant OACB,(ii) shaded region.
12. In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB, (ii) shaded region. Solution: Radius of the quadrant = 3.5 cm = 7/2 cm (i) Area of quadrant OACB = (πR2)/4 cm2 = (22/7)×(7/2)×(7/2)/4 cm2 … Continue reading 12. In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the(i) quadrant OACB,(ii) shaded region.
11. On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.
11. On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief. Solution: Number of circular designs = 9 Radius of the circular design = 7 cm There are three circles in one side of square handkerchief. ∴ Side … Continue reading 11. On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.
9. In Fig. 12.27, 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.
9. In Fig. 12.27, 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. Solution: Radius of larger circle, R = 7 cm Radius of smaller circle, r … Continue reading 9. In Fig. 12.27, 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.
14. Tick the correct solution in the following:Area of a sector of angle p (in degrees) of a circle with radius R is(A) p/180 × 2πR(B) p/180 × π R2(C) p/360 × 2πR(D) p/720 × 2πR2
14. Tick the correct solution in the following: Area of a sector of angle p (in degrees) of a circle with radius R is (A) p/180 × 2πR (B) p/180 × π R2 (C) p/360 × 2πR (D) p/720 × 2πR2 Solution: The area of a sector = (θ/360°)×πr2 Given, θ = p So, area … Continue reading 14. Tick the correct solution in the following:Area of a sector of angle p (in degrees) of a circle with radius R is(A) p/180 × 2πR(B) p/180 × π R2(C) p/360 × 2πR(D) p/720 × 2πR2
13. A round table cover has six equal designs as shown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per cm2 . (Use √3 = 1.7)
13. A round table cover has six equal designs as shown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per cm2 . (Use √3 = 1.7) Solution: Total number of equal designs = 6 AOB= 360°/6 = 60° Radius … Continue reading 13. A round table cover has six equal designs as shown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per cm2 . (Use √3 = 1.7)
12. To warn ships for underwater rocks, a lighthouse spreads a red colored light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned.
12. To warn ships for underwater rocks, a lighthouse spreads a red colored light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π = 3.14) Solution: Let O bet the position of Lighthouse. Here the radius will be … Continue reading 12. To warn ships for underwater rocks, a lighthouse spreads a red colored light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned.
11. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.
11. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades. Solution: Given, Radius (r) = 25 cm Sector angle (θ) = 115° Since there are 2 blades, The total … Continue reading 11. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.
10. An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella
10. An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella. Solution: The radius (r) of the umbrella when flat = 45 cm So, the area of the circle (A) = … Continue reading 10. An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella
9. 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 Fig. 12.12. Find:(i) the total length of the silver wire required.(ii) the area of each sector of the brooch.
9. 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 Fig. 12.12. Find: (i) the total length of the silver wire required. (ii) the area of each … Continue reading 9. 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 Fig. 12.12. Find:(i) the total length of the silver wire required.(ii) the area of each sector of the brooch.
8. A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11). Find(i) the area of that part of the field in which the horse can graze.(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)
8. A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11). Find (i) the area of that part of the field in which the horse can graze. (ii) the increase in the grazing area … Continue reading 8. A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11). Find(i) the area of that part of the field in which the horse can graze.(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)
7. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. (Use π = 3.14 and √3 = 1.73)
7. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. (Use π = 3.14 and √3 = 1.73) Solution: Radius, r = 12 cm Now, draw a perpendicular OD on chord AB and it will bisect chord … Continue reading 7. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. (Use π = 3.14 and √3 = 1.73)
6. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)
6. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73) Solution: Given, Radius = 15 cm θ = 60° So, Area of sector OAPB = (60°/360°)×πr2 cm2 … Continue reading 6. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)
5. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:(i) the length of the arc(ii) area of the sector formed by the arc(iii) area of the segment formed by the corresponding chord
5. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (i) the length of the arc (ii) area of the sector formed by the arc (iii) area of the segment formed by the corresponding chord Solution: Given, Radius = 21 cm θ = 60° (i) Length of … Continue reading 5. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:(i) the length of the arc(ii) area of the sector formed by the arc(iii) area of the segment formed by the corresponding chord
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