Question

The clock has a diameter of 18 inches. At 8 o'clock, what is the area of the sector formed by the two hands of the clock? Round to the nearest tenth.

Answer 1

The area of the sector is 84.8 in.² to the nearest tenth

Explanation:

∵ the clock is a circle

∴ The measure of angles between each two hours = 360° ÷ 12 = 30°

∵ At 8 o'clock the hour hand pointed on 8 and the minute hand pointed on 12

∴ There are 4 angles between the two hands

∴ The central angle subtended by the arc = 4 × 30° = 120°

∵ The Area of the sector =
`(x)/(360) \pi r^(2)` where x is the central angle subtended by this arc

∴ Area sector =
`(120)/(360)` × π × (18/2)²

∴ Area sector =
`(1)/(3)` × π ×81 = 27π = 84.8 in² to the nearest tenth