F.3 maths X2

If the original length of square = x, then
then new length of square = (1+20%)x = 1.2x

the original area of square = x^2
the new area of square = (1.2x)^2=1.44x^2

the percentage change in the area of the square
=(1.44x^2-x^2)*100%/(x^2)
=+44%

If the original radius of circle = r, then
then new radius of circle = (1-15%)r = 0.85r

the original area of circle = pi*r^2
the new area of circle = pi*(0.85r)^2=0.7225*pi*r^2

the percentage change in the area of the square
=(0.7225pi*r^2-pi*r^2)*100%/(pi*r^2)
=-27.75%

Ans for 1)
Area of Sqaure = x^2
When the length increased by 20%,
its area will be changed to,

= (x(1+20%))^2
= (1.2x)^2
= 1.44x^2

Precentage change in area
= 1.44x^2 - x^2
= 1.44x^2 - 1x^2
= 0.44
= 44%


Ans for 2)
Area of circle = TTr^2

Its radius reduced by 15%,
its area will be changed to,
= TT(r(1-15%)^2)
= TT(0.85r)^2
= 0.7225r^2TT

Precentage change in area,
= TTr^2 - 0.7225r^2TT
= 0.2775
= 27.75%

1. Let x be the length of one side of the original square.
Original area of the square = x^2
New length of the square = x(1+20%) = 1.2x
New area = 1.2x * 1.2x = 1.44x^2
Hence percentage change required = (1.44x^2 -x^2)/x^2 * 100% = +44%
Therefore, the percentage increase is 44%.

2. Let r be the original radius of the circle.
Original area = pi*r^2
New radius = r(1-15%) = 0.85r
New area = pi*(0.85r)^2 = 0.7225pi*r^2
Percentage change = (0.7225pi*r^2-pi*r^2)/pi*r^2 x 100% = -27.75%
Therefore, the percentage decrease is 27.75%