a bicycle wheel makes 75 revolutions per min. to maintain a speed of 8.91km/hr. find the diameter of the wheel..??

Given that:-

Bicycle wheel makes 75 revolutions per minute.

Speed of wheel = 8.91 km/hr.

Let radius of wheel = r km.

We know that-

Distance covered in one revolution of the wheel = circumference of the wheel.

                                                                           = 2πr km

∴ Distance covered in one minute = 2πr ×75

                                                     = 150πr km.

Hence, Distance covered in one hr = 150πr × 60 km.

By given condition-

Speed of wheel = 8.91 km/hr

or r = 0.315 m                 [∵ 1 km = 1000 m]

or r = 31.5 cm                 [∵ 1 m = 100 cm]

Hence Diameter of wheel = 2 × r

 = 2 × 31.5 cm

 = 63 cm