Question

if the radius of a circle is increased by 10% then the percent increase in its area is?​

Answer 1

Let the radius of circle= 70 cm

Area of circle= πr²

=22/7 ×70cm×70cm

=15400 cm²

10% increase in radius=10/100 ×70cm

=7 cm

New radius=70 cm+7cm

=77 cm

New area=πr²

=22/7×77cm×77cm

=18634cm²

Increase in area=18634cm²-15400cm²

=3234cm²

increase% in area=(3234/15400 )×100%

=21

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Answer 2

Answer- The above question is from the chapter 'Areas Related to Circles'.

Concepts Used: 1) Area of circle = πr²

2) Increase in radius = % age × original radius

3) New radius = Increase in radius + Original radius

4) Increase in area = New area - Original area

5) Increase % of area = $\frac{Increase \: in \: area}{Original \: area}$ × 100

Given question: If the radius of a circle is increased by 10%, then the percent increase in its area is ___ .

Solution: Let r be the radius of circle.

Area of circle = πr²

Increase in radius = % age × original radius

Increase in radius = $\frac{10}{100}$ × r

Increase in radius = $\frac{r}{10}$

New radius = Increase in radius + Original radius

New radius = $\frac{r}{10}$ + r

New radius = $\frac{11r}{10}$

New area = π $\frac{11r}{10}$ × $\frac{11r}{10}$

New area = πr² $\frac{121}{100}$

Increase in area = New area - Original area

Increase in area = πr² $\frac{121}{100}$ - πr²

Increase in area = πr² × $\frac{21}{100}$

Increase % of area = $\frac{Increase \: in \: area}{Original \: area}$ × 100

Increase % of area = [ πr² × $\frac{21}{100}$ ÷ πr² ] × 100

Increase % of area = 21 %

∴ If the radius of a circle is increased by 10%, then the percent increase in its area is 21%.