The minute hand of a clock is $20 \mathrm{~cm}$ long. Find the area on the face of the clock swept by the minute hand between 8 a.m. and $8: 45$ a.m. |
$\frac{6600}{7} \mathrm{~cm}^2$ $\frac{6600}{9} \mathrm{~cm}^2$ $\frac{6600}{18} \mathrm{~cm}^2$ $\frac{6600}{14} \mathrm{~cm}^2$ |
$\frac{6600}{7} \mathrm{~cm}^2$ |
We know that, Area of a sector = πr2 × \(\frac{ θ }{360}\) We have, The length of the minute hand of a clock = 20 cm As we know in the 1-minute angle made by the minute hand = 6° So, in 45 min the minute hand will make 45 × 6 = 270° Area = π × 202 × \(\frac{ 270 }{360 }\) = \(\frac{22}{7}\) × 400 × \(\frac{ 270 }{360 }\) = $\frac{6600}{7} \mathrm{~cm}^2$ |