Question

The length of the minute hand of a clock is $14\mathrm{cm}$. Find the area swept by the minute hand in $5$ minutes.

Answer 1

Calculate the area.

Let us assume that,

The minute hand of the clock acts as the radius of the circle.

So that, $\mathrm{Radius}\left(\mathrm{r}\right)=14\mathrm{cm}$

Angle rotated by min⁡ hand in $5$ minutes is computed as,

$$\begin{gathered} \theta =\frac{360}{60}\times 5 \\ \Rightarrow =30° \end{gathered}$$

Area of swept middle hand is computed as,

$$\begin{gathered} \therefore \mathit{A}\mathbf{=}\frac{\mathbf{\pi }{\mathbf{r}}^{\mathbf{2}}}{\mathbf{360}}\mathbf{\times }\mathit{\theta } \\ =\frac{{\mathrm{\pi r}}^2}{360°}\times 30° \\ =\frac{1}{12}\times \frac{22}{7}\times {\left(14\right)}^2 \\ =\frac{1}{12}\times 22\times 28 \\ =51.34{\mathrm{cm}}^2 \end{gathered}$$

Hence, the area swept by the minute hand in $5$ minutes is $51.34{\mathrm{cm}}^2$.