Question

The length of the minute hand of a wall clock is 7 cm, then area swept by the minute hand in 10 minutes is ____ (use $\pi$ =$\frac{22}{7}$)

• A. 30 ${cm}^2$
• B. 30.66 ${cm}^2$
• C. 28.69 ${cm}^2$
• D. 25.66 ${cm}^2$

Answer 1

The correct option is D 25.66 ${cm}^2$

In 1 minute, minute hand makes an angle of $6^{\circ }$
so, in 10 minutes, minute hand will make an angle of ${60}^{\circ }$

Area swept by minute hand in 10 minutes = Area of sector of radius 7 cm with angle ${60}^{\circ }$
Area of sector = $\frac{x^{\circ }}{{360}^{\circ }}$$\times$ $\pi$ $\times$ $r^2$
so,
Area swept by minute hand in 10 minutes = $\frac{{60}^{\circ }}{{360}^{\circ }}$$\times$ $\frac{22}{7}$$\times$ $7^2$
= 25.66 ${cm}^2$