Question

The length of the hour hand of a clock is 6cm.find the area of sector swept by this hour hand in90 minutes

Answer 1

Answer:

$Area of sector = \frac{ θ}{360} πr2$

$\frac{90}{360} \times \frac{22}{7} \times 6 \times 6 \\ = > \frac{1}{4} \times \frac{22}{7} \times 6 \times 6 \\ = > 28.28sq.units$

Answer 2

Answer:

99/7 cm² (or) 14.143 cm²

Step-by-step explanation:

Given that the length of the hour hand of a clock is 6 cm, therefore, we can take the radius as 6 cm.

First, we will divide 90 minutes into 60 minutes and 30 minutes.

The hour hand, in one hour, i.e., in 60 minutes, completes 1/12th part of the whole clock or circle. So the Θ will be,

Θ = (1/12)360

Θ = 30°

Now we will find the area swept by the hour hand in 60 minutes, for that we will use the sector formula, i.e.,

Area of the sector = Θ/360(πr²)

= 30/360(22/7 × 6²)

= 1/12(22/7 × 36)

= 22/7 × 3

=  66/7 cm² (or) 9.428 cm²

Now, we will find the area swept by the hour hand in 30 minutes.

The hour hand in 30 minutes completes 1/24th part of the circle or clock, so the Θ will be,

Θ = (1/24)360

Θ = 15°

Now the area swept by the hand in 30 minutes is = 15/360(22/7 × 6²)

= 1/24(22/7 × 36)

= 1/2 × 22/7 × 3

= 11/7 × 3

= 33/7 cm² (or) 4.714 cm²

Now, we will add the areaswept by the hand in 60 minuts and 30 minutes,

= 66/7 + 33/7

= 99/7  cm² (or) 14.143 cm²[answer]

Hope this helps you!!!!