Question

If the radius of a circle is increased by 30%, by what percentage the area of the circle will increase?
50%
49%
69%
75%
Hint
The increased radius will bes +
( o ) ". Find the new area and then calculate the percentage change.​

Answer 1

Given:

The radius of a circle is increased by 30%,

Solution:

Assume that the radius of the circle is $r$.

Find the initial area$\[ = \pi {r^2}\]$

Find the area after 30% increment in radius,

$\[ = \pi {\left( {\frac{{130r}}{{100}}} \right)^2}\]$

$\[ = \frac{{169}}{{100}}\pi {r^2}\]$

Now calculate the net % increase in area,

$\[ = \frac{{\frac{{169}}{{100}}\pi {r^2} - \pi {r^2}}}{{\pi {r^2}}} \times 100\]$

$\[ = \frac{{\pi {r^2}\left( {169 - 100} \right)}}{{\pi {r^2} \times 100}} \times 100\]$

$\[ = 69\% \]$

Hence the percentage the area of the circle will increase is 69%.

Answer 2

Answer:

short trick :

Step-by-step explanation:

original=100%

increase=30%

now,

original+increased/100

so, = 100+30/100

=130/100

zero - zero cut

= 13/10 = 1.3

• now, square this number (1.3)²

1.69

after point your answer is there

so, ans is 69%

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