Question

the minute hand of a clock is 21 cm long calculate the area swept by it and the distance travelled by its tip in 20 minutes​

Answer 1

Answer:

Answer is 126cm^2.

Step-by-step explanation:

126cm^2

Answer 2

Distance traveled by clock tip in 20 minutes​. = 43.98 cm.

Area swept by clock in 20 minutes. = 461.81 cm².

Given:

The minute hand of a clock is 21 cm long.

To find:

Distance traveled by clock tip in 20 minutes​.

Area swept by clock in 20 minutes.

Formula used:

Area of arc = $\frac{\text{Angle \ of \ arc\ in \ radian}}{2\pi } \times \text{Area \ of \ circle}$

Length of arc = $\frac{\text{Angle \ of \ arc\ in \ radian}}{2\pi } \times \text{ perimeter \ of \ circle}$

Explanation:

The minute hand of a clock is moving in circular arc

The minute hand of a clock is 21 cm long.

So radius of circle = 21 cm.

Angle covered by clock in 60 minute = 360°

So Angle covered by clock in 20 minute = $360 \times \frac{20}{60}$                                                                                               = 120°

                                                            = $\frac{2\pi }{3} \text{ Radian}$

This shoes that the minute hand can move 120° arc

Area of arc = $\frac{\text{Angle \ of \ arc\ in \ radian}}{2\pi }\times \text{Area \ of \ circle}$

Area of arc = $\frac{\text{Angle \ of \ arc\ in \ radian}}{2\pi } \times\pi\times\text{(Radius)}^2$

                  = $\frac{\frac{2\pi }{3} }{2\pi } \times\pi\times (21)^2$                

Area of arc = 461.81 cm².

Length of arc = $\frac{\text{Angle \ of \ arc\ in \ radian}}{2\pi }\times \text{ perimeter \ of \ circle}$

Length of arc = $\frac{\text{Angle \ of \ arc\ in \ radian}}{2\pi }\times 2 \times\pi\times\text{ (Radius)}^2$                                                        = $\frac{\frac{2\pi }{3} }{2\pi }\times 2\times\pi\times21$

Length of arc = 43.98 cm.

Therefore, the distance traveled by clock tip in 20 minutes​ is 43.98 cm and area swept by clock in 20 minutes is 461.81 cm².

To learn more....                  

1. The minute hand of a clock is 21cm long . find the distance moved by the tip of minute hand in one hour

brainly.in/question/5061875

2. The minute hand of a clock is 7 cm long. find the displacement & distance covered by it from 9:00 a.m. to 9:30 a.m

brainly.in/question/1328650