Ex 6.1, 6

Transcript

Ex 6.1, 6 If the diameter of a car tyre is 56 cm, then: (i) How far does the car need to travel for the tyre to complete one revolution? (ii) How many revolutions does the tyre make if the car travels 10 km? Circumference of wheel In 1 rotation, wheel travels distance = Circumference Circumference of wheel Diameter = 56 cm Radius of wheel = r = 56/2 = 28 cm Circumference of wheel = 2𝜋r = 2 × 𝟐𝟐/𝟕 × 28 = 2 × 22 × 4 = 44 × 4 = 176 cm Thus, in 1 rotation the wheel travels 176 cm We are also asked (ii) How many revolutions does the tyre make if the car travels 10 km? Now, Number of rotations = (𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒓𝒂𝒗𝒆𝒍𝒍𝒆𝒅)/(𝑪𝒊𝒓𝒄𝒖𝒎𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒐𝒇 𝒘𝒉𝒆𝒆𝒍) Since Circumference is in cm, we convert Distance travelled in cm Now, Distance travelled = 10km = 10 × 1km = 10 × 1,000 m = 10,000 m = 10,000 × 1 m = 10,000 × 100 cm = 10,00,000 cm Thus, Number of rotations = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑙𝑙𝑒𝑑)/(𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑤ℎ𝑒𝑒𝑙) = (𝟏𝟎,𝟎𝟎,𝟎𝟎𝟎)/𝟏𝟕𝟔 = (𝟓,𝟎𝟎,𝟎𝟎𝟎)/𝟖𝟖 = (𝟐,𝟓𝟎,𝟎𝟎𝟎)/𝟒𝟒 = (𝟏,𝟐𝟓,𝟎𝟎𝟎)/𝟐𝟐 = (𝟔𝟐,𝟓𝟎𝟎)/𝟏𝟏 = 5681.81 Thus, Wheel rotates approximately 5,681 times