Question

if the radius of circle is increased by 6 % then the area of circle is increased by ​

Answer 1

Answer : 12.36%

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Solution :

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Let, the radius of Circle = r

Then, area of Circle will be = πr²

If the radius is increased by 6% then the new radius will be :

r×106/100

Now, the area of Circle = π(106r/100)²

Now, area is increased :

$\frac{\pi {( \frac{106r}{100} )}^{2} - \pi {r}^{2} }{\pi {r}^{2} } \times 100 \\ \\ = > \frac{\pi {r}^{2}( {( \frac{106}{100} )}^{2} - 1) }{\pi {r}^{2} } \times 100 \\ \\ = > (\frac{106 \times 106}{100 \times 100} - 1) \times 100 \\ \\ = > \frac{11236 - 10000}{10000} \times 100 \\ \\ = > \frac{1236}{100} \\ \\ = > 12.36$

So, the area is increased by 12.36% after radius is increased by 6%

Answer 2

Area of a original circle = π * Radius²

= πr² units²

Increased % on radius = r(100 + Increased %)/100

= r(100 + 6)/100

= r(106/100)

= 106r/100

Area of new circle = π * Radius²

= π * (106r/100)(106r/100)

= π * (11,236r²/10000)

= π * 1.1236r²

= 1.1236πr² units²

Increase in area = Area of original circle - Area of new circle

= 1.1236πr² - πr²

= 0.1236πr² units²

Increase in area % = Increase in area/Origonal area * 100

= 0.1236πr²/πr² * 100

= 0.1236 * 100

= 12.36 %

Area of the circle is increased by 12.36 %