The minute hand of a clock is 7cm long. Find the area traced by the minute hand of the clock between 4:15pm to 4:35 pm on a day.

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

To solve this, you must first find the area of the whole clock.  As you know, the area of a circle is found by the equation

Area = pi*(r^2)

In this equation, r stands for the radius of the circle.

We will assume that the minute hand is the radius.  So then our equation is

Area = 3.14*(49)  because 49 is 7 times 7.

So the area of the whole circle is 153.86 cm^2

The area traced by the hand in the time you mention is one-third of the total area.  That is because there are 12 intervals on a clock face (5 minutes each).  The time you mention covers 4 intervals.  Therefore, the area traced is

51.29 cm^2

 

 

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The minute hand covers an area of pir^2 in 60 minutes So it covers an area of (35-15)/60 0r pir^2 =(20/60)pir^2  =

=(1/3)pi(7^2) cm^2 as the hour hand is 7cm lomg.

= 49pi/3

=51.31268001cm^2

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