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 central angle

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

Step2: Use the sector - area formula

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

Substitute \(r = 10\) and \(\theta=68\) into the formula:

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Answer:

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