Question

Find the probability that a point choseb at randon the figure will lie in the shaded region. Write your anser as a percentage rounding to the nearest hundreth in percentage form

Answer 1

21.5%

Step-by-step explanation:

Find the area of the square, which is 40² or 1600 sq m

Find the area of one circle, multiply it by 4, then subtract that from 1600

A = 100(3.14) = 314

314 x 4 = 1256

1600 - 1256 = 344

Probability of landing in the shaded region is 344/1600 = 21.5%

Answer 2

Answer: 21.46%

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Step-by-step explanation:

Let's find the area of one of the circles

A = pi*r^2

A = pi*10^2

A = 100pi

One circle is exactly 100pi square meters in area.

Four of the circles then combine to a total area of 4*100pi = 400pi square meters.

The distance along the bottom of the square is equal to two diameters, each diameter being 2r = 2*10 = 20 meters. So the distance along the bottom of the square is 2*20 = 40 meters. The square has an area of 40^2 = 1600 square meters.

The shaded region would therefore have an exact area of 1600-400pi square meters.

This approximates to 1600-400pi = 343.362938564082

Divide this over the area of the square to get the probability we want to find:

343.362938564082/1600 = 0.21460183660256

That's roughly 0.2146, which converts to 21.46%