Question

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Answer 1

Angle make by the minute hand in 1 minute = 6^∘
Angle make by the minute hand in 5 minute = 5 ⨯ 6^∘ = 30^∘
Area of the sector having central angle is given by
$$\begin{gathered} \frac{30°}{360°}\mathrm{\pi }{\left(14\right)}^2 \\ =\frac{1}{12}\times \frac{22}{7}{\left(14\right)}^2 \\ =51.33{\mathrm{cm}}^2 \end{gathered}$$
Hence, the area swept by minute hand in 5 minutes is 51.33 cm²