Area Problems
A man runs round a circular field of radius 50m at the speed of 12 km/hr. What is the time taken by the man to take twenty rounds of the field?
speed = 12 km/h = 12 × 5 18 = 10 3 m / s distance covered = 20 × 2 × 22 7 × 50 = 44000 7 m time taken = distance /speed = 44000 7 × 3 10 s e c = 4400 × 3 7 × 1 60 m i n = 220 7 m i n
Given that, area = 40 sq cm, base = 28 cm and height = perpendicular = ?Area = (base x perpendicular) / 2 ? 40 = (28 x perpendicular) / 2 ? perpendicular = 40/14 = 20/7 = 26/7 cm
Let each side of the square be a. Then, area = . a 2 New side = 125 a 100 = 5 a 4 . New area = 5 a 4 2 = 25 a 2 16 Increase in area = 25 a 2 16 - a 2 = 9 a 2 16 Increase% = 9 a 2 16 * 1 a 2 * 100 % = 56.25%.
Let the width of the room be x membersThen, its area = (4x) m2Area of each new square room = (2x)m2Let the side of each new room = y metersThen, y2 = 2xClearly, 2x is a complete square when x=2? y2 = 4? y = 2 m .
Let circumference = 100 cm . Then, ? 2?r = 100? r = 100/2? =50/?? New circumference = 105 cm Then, 2?R = 105? R = 105 / (2?)&rArr Original area = [ ? x (50/?) x (50/?) ] = 2500/? cm2? New Area = [? x (105/2?) x (105/2?)]= 11025 / (4?) cm2? Increase in area = [11025/(4?)] - 2500/? cm2= 1025 / 4? cm2Required increase percent [1025/(4?)] x 2500/? x 100 = 41/4%= 10.25%
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