Question

The minute hand of a clock is $10$ cm long. Find the area of the face of the clock described by the minute hand between $9$A.M and $9.35$A.M.

• A. $90.165c{m}^2$
• B. $112.6c{m}^2$
• C. $156.4c{m}^2$
• D. $183.3c{m}^2$

Answer 1

The correct option is D $183.3c{m}^2$

We have,
Angle described by the minute hand in one minute $=6^o$

$\therefore$ Angle described by the minute hand in $35$ minutes $=(6\times 35{)}^o={210}^o$

$\therefore$ Area swept by the minute hand in $35$ minutes.

$=$ Area of a sector of angle ${210}^o$ in a circle of radius $10$ cm

$=\frac{\theta }{360}\pi {r_1}^2$

$=\frac{210}{360}\times \frac{22}{7}\times (10{)}^{2}c{m}^2$.....

$=183.3c{m}^2$