Answer:
The minute hand of a clock is 8 inches long and moves from 12 to 2 o'clock. How far does the tip of the minute hand move? Express your answer in terms of pie and then round to two decimal places.
Step-by-step explanation:
Area covered by minute hand between 9:05 to 9:25 is equals to
[tex]\frac{4}{3} \pi[/tex] square inches.
" Area of the sector is defined as the space occupied by two radii and the arc included in it."
Formula used
Area of the sector = [tex](\pi r^{2}) \frac{\theta}{360}[/tex]
According to the question,
Area covered by minute hand between 9:05 to 9:25 forms a sector.
Total minutes = 20 minutes
60minutes = 360°
20minutes = [tex]\frac{360}{60} (20)[/tex]
= 120°
Therefore,
Central angle = 120°
radius of the circle = 2inches
Substitute the value in the formula we get,
Area of the sector formed by minute hand = [tex]\pi (2)^{2} (\frac{120}{360} )[/tex]
= [tex]\frac{4}{3} \pi[/tex]square inches
Hence, area covered by minute hand between 9:05 to 9:25 is equals to
[tex]\frac{4}{3} \pi[/tex] square inches.
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