Question

$\huge\mathfrak\red{Hello\: Mate}$

if the length of the minute hand of a clock is 28 CM then the area swept by the minute hand in 15 minutes is ?

I want Verified Answer
pls maths Aryabhatta, genius, or brainly stars pls help me​

Answer 1

Question:

If the length of the minute hand of a circular clock is 28 cm, then find the area swept by the minute hand in 15 minutes.

Answer:

The area swept by the minute hand of circular clock in 15 minutes is 616 cm².

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

We have given that,

The length of minute hand of a circular clock is 28 cm.

We have to find the area swept by the minute hand in 15 minutes.

A minute hand is joined to the centre of the clock i. e. circle.

Hence, the minute hand is radius of the circle.

When a minute hand will move in 15 minutes, it will make a right angle from the point it started moving to the point which it stopped ( completed ) 15 minutes.

Suppose, a minute hand is on 12.

After 15 minutes, it will be on 3.

The angle between 12 & 3 in a clock is a right angle.

From this information, it is clear that,

We have to find the area of the sector made by the minute hand in a circular clock i. e. Area of the shaded region in the figure.

$\bullet\sf\:\theta\:=\:90^{\circ}\\\\\\\bullet\sf\:radius\:(\:r\:)\:=\:28\:cm$

Now, we know that,

$\pink{\sf\:Area\:of\:sector\:=\:\dfrac{\theta}{360}\:\times\:\pi\:r^2}\sf\:\:\:-\:-\:[\:Formula\:]\\\\\\\implies\sf\:Area\:of\:sector\:=\:\dfrac{\cancel{90}}{\cancel{360}}\:\times\:\dfrac{22}{7}\:\times\:(\:28\:)^2\\\\\\\implies\sf\:Area\:of\:sector\:=\:\dfrac{1}{4}\:\times\:\dfrac{22}{\cancel7}\:\times\:28\:\times\:\cancel{28}\\\\\\\implies\sf\:Area\:of\:sector\:=\:\dfrac{1}{\cancel4}\:\times\:22\:\times\:28\:\times\:\cancel{4}\\\\\\\implies\sf\:Area\:of\:sector\:=\:22\:\times\:28\\\\\\\implies\boxed{\red{\sf\:Area\:of\:sector\:=\:616\:cm^2}}$

The area swept by the minute hand in 15 minutes is 616 cm².

Answer 2

Step-by-step explanation:

here is you answer in above attachment