Question

A circular watch has a minute hand that is 2.5 cm long.

(a) What distance does the tip of the hand move through in 20 minutes?
(b)What area of the watch face is covered by the minute hand in 30 minutes?

Answer 1

`L=(5)/(3) \pi cm. \\ A=3.125\pi cm^(2)`

Explanation:

a)

L - is how far does the tip of the hand move in diameter.

m - is how much time does the tip of the hand move in minutes.

m=20

r =2,5cm

`L=(m)/(60) *2\pi r\\L=(20)/(60) *2\pi *2,5cm\\L=(5)/(3) \pi cm`

In a formula, we have
`(m)/(60)` because the minute hand needs 60 minutes to make one circle. L = 2πr is a formula for the full length of a circle.

b)

A- Area

r=2,5cm

m - is how much time does the tip of the hand move in minutes.

`A=(m)/(60) *\pi r^(2) \\A=(30)/(60) *\pi *(2,5cm)^(2) \\A=(1)/(2) *\pi *6.25cm^(2) \\A=3.125\pi cm^(2)`

In the formula, we have
`(m)/(60)` because the minute hand needs 60 minutes to make one circle. The formula for the full area of a circle is A=πr².

Answer 2

a) 20 minute=2pi/3 rad

angle=arc length/radius

arc length= angle×radius

=2pi/3×2.5

=5pi/3 cm

b)area= pi(radius)²/2

=pi×6.25

=25pi/4cm²

i hope you find it helpful

Explanation: