Question

the length of a minute hand of a clock is 14 cm then area swept by the minute had in 5 mintute

Answer 1

ANSWER

Hint: Here, we can use the concept that when

the minute hand of the clock rotates, it circularly

sweeps the area. When the minute hand of the

clock completes one complete rotation, it sweeps

the total area of a circle with radius equal to the

length of the minute hand. So, for 60 minutes (one

complete rotation), it sweeps the area of the circle.

So, for 5 minutes it will be one-twelfth of the total

area.

Complete step-by-step answer:

Here, we have a minute hand of a clock (in the attachment) whose length is 14 cm. We need to find the area swept by the minute hand of the clock in 5 minutes. One complete rotation will sweep the circle fully with the radius of the circle being equal to the length of a minute hand in 60 minutes.

Step-by-step explanation:

We know that the period for one complete rotation of a minute hand is 60 minutes. So, the area swept by the minute hand of the clock in 60 minutes can be calculated using the formula:

Area=πr2

⇒Area=π(14cm2)

Using the value π=227 , we get :

⇒Area=227(14cm2)=22×2×14=616cm2

So, the total area swept in 60 min is 616 sq. cm.

So, the area swept in one minute is given by 61660 sq. cm.

So, we can calculate the area swept in 5 minutes by multiplying the above result with 5.

Area=61660×5= 51.3333 cm2

Note: We can directly calculate the area swept by minute hand in x minute using the formula:

Area=x60×πl2

Here, l is the length of the minute hand. Also, while doing calculations, take care of the units. Mathematical operations can only be performed if units are the same.

I HOPE MY ANSWER WILL HELP YOU