Question

The minute hand of a clock is $7cm$ long. Find the area traced by it on the clock face between $4:15$ p.m. and $4:35$ p.m.

• A. $59c{m}^2$
• B. $65c{m}^2$
• C. $51.3c{m}^2$
• D. $45c{m}^2$

Answer 1

The correct option is C $51.3c{m}^2$

Time $=20$ min

Angle made by minute hand in 1 minute $=\frac{{360}^0}{{60}^0}=6^0$

$\therefore$ In $20$ min $=6^0\times 20={120}^0$

$\therefore$ Area swept $=\frac{\theta }{{360}^0}\times \pi r^2=\frac{{120}^0}{{360}^0}\times \frac{22}{7}\times 7\times 7=\frac{154}{3}=51.3{cm}^2$