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State true or false.

The minute hand of a clock is 15 cm long. Then, the area swept by it in 20 minutes will be $235.5 cm 2$ .

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True

False

answer is A.

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Detailed Solution

We have to check if the area swept by it in 20 minutes will be

235.5 cm 2

, given that the minute hand of a clock is 15 cm long.
Note that angle inscribed by the minute hand in 60 minutes

= 360 °

So, the angle inscribed by the minute hand in 20 minutes:

= 36060 × 20 = 120 °

Area of the sector

= π r 2 θ 360

Calculating the required area.
Note that, the required area swept by the minute hand in 20 minutes = Area of the sector

= 3.14 × 15 × 15 × 120360 = 235.5 cm 2

∴ The required area is 235.5 cm 2 .

Thus, the statement is true.
Therefore, option 1 is correct.

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