Question

The minute hand of a clock is $8cm$ long. Find the area swept by the minute hand between $8.30a.m.$ and $9.05a.m.$

• A. $117\frac{1}{3}c{m}^2$
• B. $107\frac{1}{3}c{m}^2$
• C. $217\frac{1}{3}c{m}^2$
• D. None of these

Answer 1

The correct option is A $117\frac{1}{3}c{m}^2$

Angle made the centre by each $5$ minutes =$\frac{360}{12}$
=${30}^o$

Angle covered between $8.30$am to $9.5$a.m is ${210}^o$

Therefore,
$Area=\pi (8{)}^2\frac{210}{360}$
$=\frac{22}{7}\times 8\times 8\times \frac{210}{360}$
$=117\frac{1}{3}c{m}^2$