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.
A square, a circle and equilateral triangle have same perimeter. Consider the following statements. I. The area of square is greater than the area of the triangle. II. The area of circle is less then the area of triangle. Which of the statement is/are correct?
Let the radius of circle is 'r' and a side of a square is 'a', then given condition2?r = 4a ? a = ?r/2? Area of square = (?r/2)2 = ?2 /4r2 = 9.86r2/4 = 2.46r2and area of circle = ?r2 = 3.14;r2and let the side of equilateral triangle is x.Then, given condition,3x = 2?r ? x = 2?r/3? Area of equilateral triangle = ?3/4 x 2= ?3/4 x 4?2r2/9= ?2/3?3r2= 1.89r2Hence, Area of circle > Area of square > Area of equilateral triangle.