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Q.

You are required to create a model of a circular wall clock and paste the numbers from 1 to 12 on its dial. What is the angle made at the center between 3 and 7? Find the area of this region, if the length of the minute hand of the clock is 21 cm.

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a

140 °

and 1252

c m 2

b

130 °

and 352

c m 2

c

120 °

and 462

c m 2

d

150 °

and 587

c m 2

answer is C.

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Detailed Solution

Given that we have to create a model of a circular wall clock and paste the numbers from 1 to 12 on its dial.
We have to find the angle made at the center between 3 and 7 and have to find the area of this sector.
The expression to find the area of a sectors,

A = θ 360 ° π r 2

. Here

r

is the radius.
The required figure geometry is shown below,
Question Image

Question Image

The length of a minute hand of a clock is given as

cm .
There are 12 points and the angle formed by every pair of points at the center will be some

x o

.
We know that the sum of the angle that lie between pair of numbers is

360 o

.
Thus, the angle that is formed by each of the twelve numbers on the clock is,

x o = 360 ° 12 ⇒ x o = 30 °

Between 3 and 7, there are 4 such pairs. Then, the angle between 3 to 7 is,

θ = 4 × 30 ° ⇒ θ = 120 °

So, the area swept by the minute hand between

3 to 7

is,

Question Image

The value for central angle is

120 °

and the area of the region is 462

c m 2

.
Therefore, the correct option is 3.

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