Question

19. The length of the minute hand of a clock is 21cm. Find the area swept by the minute hand in half an hour

Answer 1

Answer:Let's consider an hour circle. An hour circle is a circle who's dimensions are measured in terms of minutes. The entire clock is a Total of 60 minutes in area.

So, the area covered by any radius is the fraction (of minutes out of the total 60 minutes) of the circle. The area with the radius 21cm in this case = (30/60)×π×(21cm)²

the area swept=693 cm^2

Answer 2

$\red{\huge{\boxed{\sf{Given:}}}}$

The length of the minute hand of a clock is 21 cm.

$\red{\huge{\boxed{\sf{To\:\:be\:\:found:}}}}$

The area swept by the minute hand in half an hour.

Now,

For half hour it will make 180°

So, it makes a sector.

Radius = 21 cm (minute hand of the clock)

Angle = $\theta$ = 180°

Area of the sector

$\boxed{\boxed{\bf = \dfrac{\theta}{360} \times \pi r^2 }}$

So,

$\bf = \frac{180}{360} \times \frac{22}{7} \times 21 \times 21$

$\bf = \frac{1}{2} \times \frac{22}{7} \times 21 \times 21$

[divide 22 by 2 and 21 by 7]

$\bf = 11 \times 3 \times 21$

$\bf = 693 cm^{2}$

Hence,

Area of the sector i.e area swept by the minute hand in half an hour = 693cm²