Question

If the radius of a circle is decreased by 50%, its
area is reduced by​

Answer 1

Answer:

75%

Explanation:

Let r be the radius

So, area of circle will be.

$\pi \: r {}^{2}$

so, if 50% is decreased

so ,. new will be

$r - \frac{50}{100} \times r$

$= \frac{50}{100} \times r$

new area of circle will be

$\pi \:( \frac{50}{100} \times r ) {}^{2}$

$= \pi \: \frac{ {r}^{2} }{4}$

SO, CHANGE IN AREA OF CIRCLE WILL BE

$\pi \: {r}^{2} - \pi \: \frac{ {r }^{2} }{4}$

$= \frac{3\pi {(r)}^{2} }{4}$

SINCE PREVIOUS AREA IS GREATER THAN THE

NEW AREA , THERE IS A DECREASE

Therefore, percent decrease will be

$\frac{ \frac{3\pi( {r)}^{2} }{4} }{\pi \: {(r)}^{2} } \times 100$

i.e.

$75\%$

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