Area Problems
A man riding a bicycle, completes one lap of a circular field along its circumference at the speed of 14.4 km/h in 1 min 28 s. What is the area of the field?
The man takes 3600 s for 14.4 km The man will take 88 s for 14.4 x (88/3600) = 352/1000 km = 352 m Now, circumference of circular field = 352 m ? 2?r = 352 m2 x (22/7) x r = 352 ? r = 56 m Therefore, area of the field = ?r2= (22/7) x 56 x 56 = 8 x 22 x 56 m2= 9856 sq m.
Let breadth = b meters. then, length = 3b/2 meters ? b x 3b/2 = 2/3 X 10000? b2 = (4 x 10000)/9? b = ( 2 X 100)/3 m ? Length = (3/2) x (2/3) x 100 m= 100 m
Let the side of the square = 100 m So area of square = 100 x 100 = 10000.New length = 140 m, New breadth = 130 mIncrease in area = [(140 x 130) - (100 x 100)] m2= 8200 m2? Required increase percent = (8200/ 10000) x 100 % = 82%
Area of the park = (60 x 40) m2 = 2400 m2. Area of the lawn = 2109 m2. ∴ Area of the crossroads = (2400 - 2109) m2 = 291 m2. Let the width of the road be x metres. Then, 60x + 40x - x2 = 291 ⟹ x2 - 100x + 291 = 0 ⟹ (x - 97)(x - 3) = 0 ⟹ x = 3
Circular piece is 4 x 11 = 44 cm long, Then Circumference of circle is given by, 44 = pi x D, where D is the diameter D = 44 / pi Take pi = 22 / 7, then D = 44 / (22/7) = (44 x 7) / 22 D = 14 cm.
EXAMIANS