(a) If a wheel of a bus has diameter 84 cm , find the distance covered by the bus in 12 revolutions. (b) A boy is running along the circumference of a circular track whose radius is 35 m . Find the distance covered by him to complete four rounds. A wheel of a van is making 400 revolutions per minute. If the diameter of the wheel is 70 cm find its speed. ANSWERS \( \begin{array}{llllll}\text { (c) Semicircle } & \text { (b) Minor sector } & \text { (c) Minor segment } & \text { 2. to 3. Show to your teacher. } \\ \begin{array}{lllll}\text { (a) } \\ \text { (a) radius } & \text { (b) chord } & \text { (c) diameter } & \text { (d) minor arc } & \text { (e) major a } \\ \text { (f) semicircle } & \text { 5. } & \text { a, c, d, e,f } & \text { 6. } & \text { (a) Yes }\end{array} & \text { (b) Yes }\end{array} \)

Let's solve each part of the problem step by step. ### (a) Distance covered by the bus in 12 revolutions 1. **Find the radius of the wheel:** \[ \text{Diameter} = 84 \text{ cm} \implies \text{Radius} = \frac{84}{2} = 42 \text{ cm} \] 2. **Calculate the circumference of the wheel:** \[ \text{Circumference} = 2 \pi r = 2 \pi \times 42 \text{ cm} \approx 2 \times 3.14 \times 42 \approx 263.76 \text{ cm} \] 3. **Calculate the distance covered in 12 revolutions:** \[ \text{Distance} = \text{Circumference} \times \text{Number of Revolutions} = 263.76 \text{ cm} \times 12 \approx 3165.12 \text{ cm} \] Thus, the distance covered by the bus in 12 revolutions is approximately **3165.12 cm**. ### (b) Distance covered by the boy to complete four rounds 1. **Find the circumference of the circular track:** \[ \text{Radius} = 35 \text{ m} \implies \text{Circumference} = 2 \pi r = 2 \pi \times 35 \text{ m} \approx 2 \times 3.14 \times 35 \approx 219.8 \text{ m} \] 2. **Calculate the distance covered in four rounds:** \[ \text{Distance} = \text{Circumference} \times \text{Number of Rounds} = 219.8 \text{ m} \times 4 \approx 879.2 \text{ m} \] Thus, the distance covered by the boy to complete four rounds is approximately **879.2 m**. ### (c) Speed of the van 1. **Find the radius of the wheel:** \[ \text{Diameter} = 70 \text{ cm} \implies \text{Radius} = \frac{70}{2} = 35 \text{ cm} \] 2. **Calculate the circumference of the wheel:** \[ \text{Circumference} = 2 \pi r = 2 \pi \times 35 \text{ cm} \approx 2 \times 3.14 \times 35 \approx 219.8 \text{ cm} \] 3. **Calculate the distance covered in one minute (400 revolutions):** \[ \text{Distance in one minute} = \text{Circumference} \times \text{Number of Revolutions} = 219.8 \text{ cm} \times 400 \approx 87920 \text{ cm} \] 4. **Convert the distance to meters:** \[ 87920 \text{ cm} = \frac{87920}{100} = 879.2 \text{ m} \] 5. **Calculate the speed in meters per minute:** The speed of the van is **879.2 m/min**. To summarize: - (a) Distance covered by the bus in 12 revolutions: **3165.12 cm** - (b) Distance covered by the boy to complete four rounds: **879.2 m** - (c) Speed of the van: **879.2 m/min**