Subjects geometry

Wheel Distance Rotation 87Da1C

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1. **State the problem:** A wheel with diameter 60 cm is rolled 5 times along a straight path. We need to find the distance travelled by the wheel and the degrees the pin rotates after 5 rolls. 2. **Formula for distance travelled:** The distance travelled by one full rotation of the wheel equals the circumference of the wheel. The circumference $C$ of a circle is given by: $$C = \pi \times d$$ where $d$ is the diameter. 3. **Calculate the circumference:** $$C = \pi \times 60 = 60\pi \text{ cm}$$ 4. **Distance travelled after 5 rolls:** $$\text{Distance} = 5 \times 60\pi = 300\pi \text{ cm}$$ 5. **Calculate degrees rotated by the pin:** Each full rotation corresponds to $360^\circ$. After 5 rolls, the pin rotates: $$5 \times 360^\circ = 1800^\circ$$ **Final answers:** - Distance travelled: $300\pi$ cm (approximately 942.48 cm) - Degrees rotated by the pin: $1800^\circ$
60 cmpin