Question

if the percentage increse in the area of circle is 44% what will be the percentage increase in its circumference?​

Answer 1

Answer:

20%

Step-by-step explanation: Let the original radius be 'r' and new radius be 'R'.

Given, % increases in area = 44%

⇒ [New area - area]/area *100% = 44%

⇒ [πR² - πr²]/πr² * 100 = 44

⇒ [R² - r²]/r² = 44/100

⇒ [R² - r²]/r² = 11/25

⇒ 25[R² - r²] = 11r²

⇒ 25R² - 25R² = 11r²

⇒ 25R² = 36r²

Square-root on both sides,

 ⇒ 5R = 6r      ⇒ R = 6r/5

∴ % increase in circumference is:

         ⇒ [2πR - 2πr]/2πr * 100%

         = 2π(R - r)/2πr * 100%

         = (R - r)/r  * 100%

         = [(6r/5) - r]/r *100%

         = [ (6r - 5r)/5 ]/r * 100%

         = [ 1/5 ] * 100%

         = 20%

Answer 2

Answer:

$\large \dag$ Question :-

If the percentage increase in the area of tge circle is 44%.What will be the percentage increase in its circumstance.

$\sf\tt\large{\red {\underline {\underline{⚘\;Answer:}}}}$

$\sf\tt\large{\purple {\underline {\underline{⚘\;The \;percentage \;increase \;in \;its \;circumstances \;is \;20 percentage:}}}}$

$\large \dag$ Solution:-

Hey mate ,

First let verify your questions and next enter to calculations.

In the question given that if the percentage increase in the area of the circle is 44% .We should find (What will be the percentage increase in its circumstances. )

So,

to find this we know that,

$\sf\tt\large{\red {\underline {\underline{\;Percentage \;increase \; in \;area \;= \;44 percentage:}}}}$

Now ,

we know ,

• [New area- area/area ×100%]=44%

Now,

• lets put the values,

But here i will directly enter to main step.

$\sf\tt\large{\blue {\underline {\underline{\;R^2- \;r^2 \; / \;r^2\:= \;44/100:}}}}$

By doing all the calculations we get that,

• 25 [R^2-r^2]=11r^2
• 25R^2-25r^2=11r^2
• 25R^2=11r^2+25r^2
• 25R^2=36r^2
• 5R=6r
• R=6r/5

Therefore,

Now,

The increase in % of circumstance .

• $\frac{2\pi(R - r)}{2\ \pi \: r} × \;100%$

• R-r/r×100%

Now,

Here put value of R.

we get that,

• 6r/5-r/r×100%

• =((6r-5r/(5r)-r)×100%

• 1/5×100%

Which can also be written as,

• 1/5×100%=20%.

Hope it helps u mate .

Thank you .