Question

a pendulum swings through an angle of 17° each second. if the pendulum is 10 cm in length and the complete swing from right to left lasts 4 seconds, what area is covered by each complete swing? round to the nearest hundredth. a. 118.68 cm² b. 5.93 cm² c. 59.34 cm² d. 14.84 cm²

Explanation:

Step1: Calculate the total angle of the swing

The pendulum swings through an angle of \(17^{\circ}\) each second and the complete swing lasts \(4\) seconds. So the total angle \(\theta=17\times4 = 68^{\circ}\)

Step2: Use the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(r = 10\) cm (length of the pendulum) and \(\theta = 68^{\circ}\)
Substitute the values into the formula: \(A=\frac{68}{360}\times\pi\times(10)^{2}\)

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Answer:

C. \(59.34\mathrm{cm}^{2}\)