Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why?

The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why?

Answers (1)

False

Solution.

Let the radius of first circle is r1 and of other is r2

The length of arcs of both circles is same.

Let the arc length = a.                                

length of arc (a)=2\pi r \times \frac{\theta }{360^{\circ}}

Area of sector of first circle = a \times \frac{r_{1} }{2}     (because area of sector = \pi r^{2}\times \frac{\theta }{360^{\circ}}=\left [ 2\pi r \times \frac{\theta }{360^{\circ}} \right ] \times \frac{r}{2} )

Area of sector of second circle = a \times \frac{r_{2} }{2}

Here we found that the area of sector is depending on radius of circles.

When the circle is same then radius is also same then the given statement is true.

But in case of different circles then the radius is also different

Hence the given statement is False.

Posted by

infoexpert24

View full answer

Similar Questions

Latest Question