Question

If the circumference of a circle increases from 4π to 8π, then find the percentage increase in the area of the circle.

Answer 1

Step-by-step explanation:

Answer with CBSE marking scheme ,

It's a three marker question

Let the previous circumference of the given circle be P 1 where as the new circumference be P 2.

1/4

Consider , the previous and new radii be r and R

1/4

Since , circumference of a circle = 2π(radius of the circle ) units

1/4

So , according to question we have

P 1/ P 2 = 4π/8π

→2πr / 2πR =1/2

→ r/R =1/2

→ 2r =R .....(1). 1/4

Since , area of a circle = π(radius)^2 sq.units

→ area of previous circle , A1= πr^2

And ,

area of new circle, A2 = πR^2=π(2r)^2 (using 1)

=4πr^2

1/2

Now , increase in area of the circle = (previous area )- (new area)=4πr^2 - πr^2= 3πr^2 .

1/2

And , Increase in percentage of the area = (Increase in area )×100/( previous area of the circle) percent

= (3πr^2/πr^2)×100 percent

= 3×100 percent

=300 percent

1 ..

(3/3) .....

Hope , it helps u

If it is asked in 2 marks

Let the previous radius be r and new radius be R .

Since , circumference of a circle = 2π(radius of a circle)

A/q,

2πr/2πR=4π/8π

r /R =4/8

→ 2r =R

(1)

Percentage increase in area = (πR^2 - π r^2)×100/πr^2 percent

= {(2r)^2- r^2}×100/r^2 percent

= r^2(4-1)×100/r^2 percent

= 300 percent

(1)

If it is asked in 4 marks

Then , after a/q u can write

P1 =2πr=4π

(1/4)

and , P2 =2πR = 8π

(1/4)

Now,

(circumference of previous circle )/(circumference of new circle )= 4π/8π

(1/2)

And continue the process done for 3 marker .

Answer 2

Answer:

The area will be quadrupled .

Step-by-step explanation:

Given :  

Circumference of the circle increases from 4π to 8π.

Circumference of a circle = 2πr

Case 1 : When circumference = 4π

C = 4π  

2πr = 4π

2r = 4

r = 4/2

r = 2  

Radius = 2  

Area of a circle,A = πr²

A = 22/7 × 2²

A = (22/7 × 4) ……. ..(1)

Case 2 : When circumference = 8π

C = 8π  

2πr = 8π

2r = 8

r = 8/2

r = 4  

Radius = 4

Area of a circle,A = πr²

A = 22/7 × 4²

A = 22/7 × 16  

A = 4 (22/7 × 4) ……. ..(2)

From eq 1 and 2 , it is clear that area is quadrupled.

Hence, its area is quadrupled.

HOPE THIS ANSWER WILL HELP YOU….