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 ?
A. $${\text{36}}\frac{2}{3}{\text{c}}{{\text{m}}^2}$$
B. $${\text{157}}\frac{1}{7}{\text{c}}{{\text{m}}^2}$$
C. $${\text{183}}\frac{1}{3}{\text{c}}{{\text{m}}^2}$$
D. None of these
Answer: Option C
Solution(By Examveda Team)
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°
$$\eqalign{ & = \frac{{\pi {r^2}\theta }}{{360}} \cr & = \left( {\frac{{22}}{7} \times 10 \times 10 \times \frac{{210}}{{360}}} \right){\text{c}}{{\text{m}}^2} \cr & = \frac{{550}}{3}{\text{c}}{{\text{m}}^2} \cr & = 183\frac{1}{3}{\text{c}}{{\text{m}}^2} \cr} $$
Related Questions on Clock
The reflex angle between the hands of a clock at 10.25 is:
A. 180º
B. $${\text{192}}{\frac{1}{2}^ \circ }$$
C. 195º
D. $${\text{197}}{\frac{1}{2}^ \circ }$$
A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:
A. 145º
B. 150º
C. 155º
D. 160º
A. $$59\frac{7}{{12}}$$ min. past 3
B. 4 p.m.
C. $$58\frac{7}{{11}}$$ min. past 3
D. $$2\frac{3}{{11}}$$ min. past 4
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