Question

the boundary of the shaded region consists of four semi circular arcs .the smallest two being equal.if the diameter of the largest is 14 cm and of the smallest is 3.5 cm find the area of the shaded region

Answer 1

radius of smallest semicircular arcs
                  r = 3.5/2
                 r = 1.75 Cm

radius of largest semicircular arcs
                  r' = 14/2
                  r' = 7 Cm

Area of 2 small arcs
                 A = 2 * pi/2 r^2
                    = 3.14 * 1.75^2
                     = 9.616 Cm sq
Area of 2 large arcs
                A' = 2 * pi/2 r'^2
                    = 3.14 * 49
                    = 153.86 Cm sq
thus total area of shaded region
      
a  = A + A'
    = 9.616 + 153.86
   = 163.47 Cm sq