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The length of minute hand of a clock is 14 cm. Find the area swept by the minute hand in one minute. (Use π = 22/7) - Mathematics

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Sum

The length of minute hand of a clock is 14 cm. Find the area swept by the minute hand in one minute. (Use π = 22/7)

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Solution

Clearly, minute hand of a clock describes a circle of radius equal to its length i.e., 14 cm.

Since the minute hand rotates through 6º in one minute. Therefore, area swept by the minute hand in one minute is the area of a sector of angle 6º in a circle of radius 14 cm.

Hence, required area A is given by

`A=\frac{\theta }{360}\times \pi r^{2}`

`A={ \frac{6}{360}\times \frac{22}{7}\times (14)^{2}}`

`A={ \frac{1}{60}\times \frac{22}{7}\times 14\times 14}=\frac{154}{15}`

= 10.26 cm2

Concept: Circumference of a Circle
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