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What is the area of the face of a clock described by its minutes hand between 9 am and 9 : 35 am, if the minutes hand is 10 cm long ?

What is the area of the face of a clock described by its minutes hand between 9 am and 9 : 35 am, if the minutes hand is 10 cm long ? Correct Answer $${\text{183}}\frac{1}{3}{\text{c}}{{\text{m}}^2}$$

Angle swept by the minute hand in 35 minutes.
$$\eqalign{ & = {\left( {\frac{{360}}{{60}} \times 35} \right)^ \circ } \cr & = {210^ \circ } \cr} $$
∴ Required area = Area of a sector of a circle with radius 10 cm and central angle 210°
$$\eqalign{ & = \frac{{\pi {r^2}\theta }}{{360}} \cr & = \left( {\frac{{22}}{7} \times 10 \times 10 \times \frac{{210}}{{360}}} \right){\text{c}}{{\text{m}}^2} \cr & = \frac{{550}}{3}{\text{c}}{{\text{m}}^2} \cr & = 183\frac{1}{3}{\text{c}}{{\text{m}}^2} \cr} $$

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