Question

Как изменится радиус окружности ,если ее площадь уменьшить в три раза?

Answer 1

S1=πr1^2;
S2=πr2^2;
S2/S1=3;
S2/S1=πr2^2/πr1^2=(r2/r1)^2=3;
r2/r1=√3.
Радиус круга уменьшится в √3 раз, т.е. приблизительно в 1,73 раза.

Answer 2

Answer in detail. How will the radius of a circle change if its area is reduced by three times?

The radius of a circle is related to its area by the formula $$A = \pi r^2$$, where $$A$$ is the area and $$r$$ is the radius. If the area is reduced by three times, then we can write $$\frac{A}{3} = \pi r_1^2$$, where $$r_1$$ is the new radius. Solving for $$r_1$$, we get $$r_1 = \sqrt{\frac{A}{3\pi}}$$. To find how the radius changes, we can compare $$r_1$$ with $$r$$ by dividing them. We get $$\frac{r_1}{r} = \sqrt{\frac{A}{3\pi}} \div \sqrt{\frac{A}{\pi}} = \sqrt{\frac{1}{3}} \approx 0.577$$, which means that the new radius is about 57.7% of the original radius. Therefore, the radius of a circle will decrease by about 42.3% if its area is reduced by three times.