Question

the radius of circular disk is increased by 20% what is the percent increase in the area of the disk​

Answer 1

Answer:

Step-by-step explanation: If r is the radius of the disk, its area (before increase) is equal to

Pi r2

If r is increased by 20% it becomes

r + 20% r = r + (20/100) r = 4 + 0.2 r = 1.2 r

and the area (after increase) of the disk becomes

Pi (1.2 r)2 = 1.44 Pi r2

Change in area

Change = Area after increase - Area before increase = 1.44 Pi r2 - Pi r2

= Pi r2 (1.44 - 1) = 0.44 Pi r2

Percent change in area

(Change / Area before change) × 100% = (0.44 Pi r2/ Pi r2) × 100%

= 0.44 × 100% = 44%

Answer 2

Let the radius of original circle =r

∴ Area of original circle =πr

2

But, the radius of the circle is increased by 20%

∴ Radius of new circle R=

100

20r

+r=1.2r

Area of new circle =πR

2

=π(1.2r)

2

=1.44πr

2

Increased area =1.44πr

2

−πr

2

=0.44πr

2

Percentage increase in area =

πr

2

0.44πr

2

×100=44%