Question

A circular watch has a minute hand that is 2.3 m long.
What area of the watch face is traced out by the minute hand in 25 minutes?​

Answer 1

$\sf{\huge{\underline{\green{Given :-}}}}$

• A circular watch has a minute hand that is 2.3 m long.

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The area of the watch face is traced out by the minute hand in 25 minutes .

$\sf{\huge{\underline{\green{Answer :-}}}}$

According to the question,

A circular watch has a minute hand that is 2.3 m long.

The minute hand of the clock = Radius of the circle = 2.3 m

The minute hand complete one round in 60 min.

We, know that the angle around a point is 360°.

Hence, clock covers 360° in 60 min.

In 60 min it covers a distance of 360°.

In 1 min it covers = 360/60 = 6°

So , in 25 mins it covers = 25 × 6 = 150°

We got,

θ = 150°

➝ r = $\dfrac{\pi}{180} \times 240$

➝ r = $\dfrac{4\pi}{3}$

We know that,

l = r θ

➝ 2.3 × $\dfrac{4 \: \pi}{3}$

➝ 2.3 × $\dfrac{4 \times 22}{3 \times 7}$

➝ 2.3 × $\dfrac{88}{21}$

➝ 2.3 × 4.19

➝ 9.63 cm