Question

if diameter of a circle is increased by 30%, by what present will area of the circle increased?

Answer 1

Here you go.......

Take the diameter as x

So radius =x/2

Find old area, find new are ie, when diameter is increased by 30%

% circle increase=( New area-old area)/old area*100

The answer will be 69% increase

Hope it helps..........

plse mark me as brainliest......

Answer 2

Given: the diameter of a circle increases by 30%

To Find: by what percentage will the area of the circle increase

Answer:

  Let x be the diameter of the circle

  then radius = $\frac{x}{2}$

          the former area of the circle = $\pi r^{2}$

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

  The new diameter of the circle = (30% of the old diameter) + old diameter

                                                       = (30% × x) + x                                          

                                                       = $\frac{30x}{100}$ + x

                                                       = $\frac{3x}{10}$ + x

                                                       = $\frac{13x}{10}$

new radius = $\frac{13x}{20}$

new area of the circle = $\pi r^{2}$

                                    = $\pi (\frac{13x}{20}) ^{2}$

                                    = $\pi \frac{169}{100} x^{2}$

                                    = $\frac{169}{100} \pi x^{2}$

Increase in area of the circle = new area - old area

                                                = $\frac{169}{100} \pi x^{2}$ - $\pi \frac{x^{2}}{4}$

                                                = $(\frac{169}{100} - \frac{1}{4}) \pi x^{2}$

                                                = $(\frac{676-100}{400})\pi x^{2}$

                                                = $\frac{576}{400} \pi x^{2}$

                                                = $\frac{36}{25} \pi x^{2}$

Percentage of increase in area

                                               = $\frac{\frac{36}{25} \pi x^{2}}{\pi x^{2} }$ × 100

                                               = $\frac{36}{25}$× 100

                                               = 36 × 4

                                               = 144%

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