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? (Pi = 3.14)

Answer 1

hope you understood this question

Answer 2

Assuming that the clock is circular, the length of the minute hand is the radius.

The distance that the tip of the minute hand moves in a given time is the length of an arc along the circle.

If s is the length of arc, then s = rθ, where r is the radius and θ is the measure (in radians) of the central angle formed by the initial position and the final position of the minute hand (measured clockwise).

(a)

r = 2.5"

20 minutes is 1/3 of an hour.

Since there are 2π radians in 1 rotation of the minute hand (1 hour),

θ = (1/3)(2π) = 2π/3.

So, s = rθ = (2.5")(2π/3) = 10π/3 inches ≈ 5.24"

(b)

A = π x ^ 2 x 2

3.14 x 15 x 15 = 706.5

The area of the watch face is covered by the minute hand in 30 minutes is 706.5