Question 9 - End-of-Chapter Exercises - Chapter 6 Class 9 - Measuring Space: Perimeter and Area (Ganita Manjar

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Question 9 The wheel of a car has an outer radius of 28 cm. Calculate how far the car travels after one complete turn of the wheel, and how many times the wheel turns during a journey of 1 km. Circumference of wheel In 1 rotation, wheel travels distance = Circumference Circumference of wheel Radius = 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 How many times the wheel turns during a journey of 1 km Now, Number of rotations = (𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒓𝒂𝒗𝒆𝒍𝒍𝒆𝒅)/(𝑪𝒊𝒓𝒄𝒖𝒎𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒐𝒇 𝒘𝒉𝒆𝒆𝒍) Since Circumference is in cm, we convert Distance travelled in cm Now, Distance travelled = 1 km = 1 × 1km = 1 × 1,000 m = 1,000 m = 1,000 × 1 m = 1,000 × 100 cm = 1,00,000 cm Thus, Number of rotations = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑙𝑙𝑒𝑑)/(𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑤ℎ𝑒𝑒𝑙) = (𝟏,𝟎𝟎,𝟎𝟎𝟎)/𝟏𝟕𝟔 = (𝟓𝟎,𝟎𝟎𝟎)/𝟖𝟖 = (𝟐𝟓,𝟎𝟎𝟎)/𝟒𝟒 = (𝟏𝟐,𝟓𝟎𝟎)/𝟐𝟐 = (𝟔,𝟐𝟓𝟎)/𝟏𝟏 = 568.18 Thus, Wheel rotates approximately 5,68 times