The diameter of a cycle wheel is 126 cm.  A cyclist takes 16\(\frac{1}{2}\) minutes to reach the destination at a speed of 90 km/h.  How many revolutions will the wheel make during the journey? (take \(\pi \) = \(\frac{22}{7}\))

6250

Diameter = 126 cm

Radius = \(\frac{126}{2}\) = 63 cm = \(\frac{63}{100}\) mtr

Time = 16 \(\frac{1}{2}\) = \(\frac{33}{2}\) min = \(\frac{33}{2}\) × 60 sec. =33 × 30  sec

Speed = 90 km/hr = 90 × \(\frac{5}{18}\) m/sec = 25 m/sec

Total distance traveled = speed × time = 25 × 33 × 30 mtr

Total no. of Revolution = \(\frac{Total\;distance}{2\pi\ r}\)

                                = \(\frac{25\;×\;33\;×\;30}{2\;×\;\frac{22}{7}\;×\;\frac{63}{100}}\)

                                  = \(\frac{25\;×\;33\;×\;30\;×\;7\;×\;100}{2\;×\;22\;× 63}\)

                                 = 6250