# Mensuration-25

### From Homeworkwiki

**A man runs around a circle of radius 50 m at a speed of 12 km per hour. Find the time taken by him for going around it ten times.**

**(b) A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel.**

**(c) The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel**

**make in order to keep a speed of 66 km per hour.**

**Solution:** (a) Here r = 50, Circumference = 2 Π r = 2 x 50 x 3.14 = 314 m

Speed = 12 km / hr = 12 x 1000 / 60 meters / min = 200 meters / min

Therefore, Distance traveled in 1 round = Circumference = 314 m

Distance traveled in 10 rounds = 10 x 314 m = 3140 m

Therefore, Time taken in making 10 rounds = Distance / Speed = 3140 / 200 = 15.7 minutes

(b) 11 km = 11 x 1000 x 100 cm

Distance moved by the wheel in 1 revolution = Total distance covered / Total number of revolution

= 11 x 1000 x 100 / 5000 cm = 220 cm

Therefore, Circumference of the wheel = 220 cm

=> 2 Π r = 220

=> 2 x 22 / 7 x r = 220

=> r = 220 x 7 / (2 x 22) = 35 cm

Therefore, Diameter of the wheel = 2r = 2 x 35 cm = 70 cm

(c) Speed of the wheel = 66 km / hr

Therefore, Distance covered by the wheel in one minute =66 x 1000 x 100) / 60 cm = 110000 cm

Diameter of the wheel = 140 cm; Hence, its radius = 70 cm

Circumference of the wheel = 2 Π r = 2 X 22/7 X 70 = 440

Therefore, Number of revolutions made by the wheel in 1 minute = Total distance traveled / circumference = 110000 / 440 = 250