The area swept by 7 cm long minute hand of a clock in 10 minutes is
The area swept by 7 cm long minute hand of a clock in 10 minutes is :
(a) 77 cm2
(b) \(12\frac{5}{6}\) cm2
(c) \(7\frac{1}{12}\) cm2
(d) \(25\frac{2}{3}\) cm2
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Correct answer is (d) \(25\frac{2}{3}\) cm2
In 1 minute, minute hand makes an angle of 6°.
So, in 10 minute, minute hand will make angle of 60°.
Area swept by minute hand in 10 minute = Area of sector of radius 7 cm with angle 60°.
Area of sector \(=\frac{\pi r^2 \theta}{360^\circ}\)
\(=\frac{22 \times (7\,cm)^2 \times 60^\circ}{7 \times 360^\circ}\)
\(=\frac{22 \times 7\,cm \times 7\,cm \times 60^\circ}{7 \times 360^\circ}\)
\(=\frac{11 \times 7}{3}\,cm^2\)
\(=\frac{77}{3}\,cm^2\)
\(=25\frac{2}{3}\,cm^2\)
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