Question

The minute hand of a clock is 12 cm. long. Find the area of the face of the clock described by the minute hand in 20 minutes

Answer 1

We know that,

$20 \: min \: = \frac{20}{60} hrs = \frac{1}{3} hrs$

Now given

radius = length of minute hand = 12 cm

The area of a circle is

$\pi \: {r}^{2}$

Where r is the radius

Now as the minute has covered one - third of the clock i.e., 20 minutes. Hence area covered while rotating is one third of the total area.

Thus area of the space covered by minute till now is

$\frac{1}{3} \times \pi {r}^{2}$

Take

$\pi = \frac{22}{7}$

Then, we have

$\frac{1}{3} \times \frac{22}{7} \times 12 \times 12 \\ = \frac{1056}{7} = 150.85$

The area covered is approximately 150.85 cm^2

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