Questions: Em uma prova de ciclismo, os atletas devem percorrer 614 metros no circuito representado na figura abaixo. Quantas voltas os ciclistas precisam completar para finalizar a prova? (Use π=3,14.) Quanto mede o raio de uma circunferência sabendo-se que um arco de comprimento 25,12 cm determina um ângulo central de 24° ? (Use π=3,14.)

Solution Steps

The circuit is composed of two straight sections of 15 meters each and two semicircles with a diameter of 10 meters each.

First, calculate the circumference of a full circle with a diameter of 10 meters: \[ \text{Circumference} = \pi \times \text{diameter} = 3.14 \times 10 = 31.4 \text{ meters} \]

Since the circuit has two semicircles, the total length of the curved sections is: \[ \text{Total curved length} = \frac{31.4}{2} + \frac{31.4}{2} = 31.4 \text{ meters} \]

Next, add the lengths of the straight sections: \[ \text{Total straight length} = 15 + 15 = 30 \text{ meters} \]

Finally, sum the lengths of the curved and straight sections to find the total perimeter: \[ \text{Perimeter} = 31.4 + 30 = 61.4 \text{ meters} \]

The total distance to be covered is 614 meters. To find the number of laps required, divide the total distance by the perimeter of the circuit: \[ \text{Number of laps} = \frac{614}{61.4} \approx 10 \]

Final Answer