Area Problems The area of circle inscribed in an equilateral triangle is 462 cm . The perimeter of the triangle is? 126 cms 42 ? 3 cms 168 cms 72.6 cms 126 cms 42 ? 3 cms 168 cms 72.6 cms ANSWER EXPLANATION DOWNLOAD EXAMIANS APP ? 22/7 x r2 = 462? r2 = (462 x 7) /22 = 147? r = 7?3 cm ? Height of the triangle = 3r = 21?3 cmNow, ? a2 = a2/4 + (3r)2? 3a2/4 = (21?3)2? a2 = (1323 x 4)/3? a = 21x 2 = 42 cm? Perimeter = 3a = 3 x 42=126 cm
Area Problems A circular disc of area 0.49 ? square meters, rolls down a length of 1.76 km. The number of revolutions it makes is? 600 400 4000 300 600 400 4000 300 ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Area = ?r2 = 0.49? ? r = 0.7 mNumber of revolutions = total distance / circumference = (1.76 x 1000) / (2 x 22/7 x 0.7) = 400
Area Problems The ratio between the length and breadth of a rectangular field is 5:4. If the breadth is 20 meters less than the length, the perimeters of the field is? none of these 280 m 260 m 360 m none of these 280 m 260 m 360 m ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Let length of rectangular field = 5y,so width = 4y.From question5y - 4y = 20m? x = 20m ? Length = (5 x 20)m = 100 mBreadth = (4 x 20) m = 80 m ? Perimeter = 2 (100 + 80 ) m = 360 m
Area Problems The ratio of the radii of two circle is 1:3 the radio of their areas is? 1:6 1:9 None of these 1:3 1:6 1:9 None of these 1:3 ANSWER EXPLANATION DOWNLOAD EXAMIANS APP The Radio of areas = area of first circle : area of 2nd circle= ?r2 / ?(3r)2= ?r2/ 9 ?r2= 1/9 = 1: 9
Area Problems If the radius of a circle be reduced by 50%. Its area is reduced by? 34.5% 65.5% 31.5% 39.5% 34.5% 65.5% 31.5% 39.5% ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Original area = ? x (r/2)2 = ?r2/4Reduction in area = ? r2 - 3? r2/4? Reduction per cent = [ 3?r2/4 x 4/(?r2) x 100 ] %= 75%
Area Problems In a triangle ABC, BC = 5 cm AC = 12 cm and AB = 13 cm. The length of a altitude drawn from B on AC is? 4 cm 6 cm 7 cm 5 cm 4 cm 6 cm 7 cm 5 cm ANSWER EXPLANATION DOWNLOAD EXAMIANS APP ? s= (13 + 5 + 12) / 2 cm = 15cms-a = 2 cm, s-b = 10 cm and s-c = 3 cm ? Area = ? (15 x 2 x 10 x 3 ) cm2= 30 cm2? (12 x h) / 2 = 30 ? h = 5 cm
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