A swimming pool is constructed in the shape of two partially overlapping identical circles. Each of the circles has a radius of 20m and each circle passes through the center of the other. Find the area of the swimming pool in square meters. Round off answer to two decimal places, do not include units.

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dinela24k · Accepted Answer

Given, a swimming pool is constructed in the shape of two partially overlapping identical circles.Each of the circles has a radius of 20 m and each circle passes through the center of the other.Now, from the data given, the picture is shown below:From the figure, we have∴cos⁡(θ)=1020⇒cos⁡(θ)=12⇒cos⁡(θ)=cos⁡(60∘)⇒θ=60∘Let, Apool be the area of the poolATriangle be the area of the triangle ABC.ASector be the area of the sector.ASegment be the area of the segment.Acircle be the area of the circle.So, ∴Asegment=ASector−ATriangle⇒ASegment=12r2(2θ)−12r2sin⁡(2θ)⇒ASegment=12(20)2[2(60∘)×2π×radians360∘−12(20)2sin⁡(2(60∘))⇒ASegment=12(20)2[2π3]−12(20)2(32)⇒ASegment=245.67m2∴APool=2Acircle−2ASector⇒APool=2(π)(20)2−2(245.67)⇒APool=2021.93412⇒APool=2021.93m2The area of the swimming pool is 2021.93.

nick1337 · Accepted Answer

Let&#039;s assume that the center of the circles is point O, and the radii of the circles are both 20 meters. Since each circle passes through the center of the other, they intersect at two points.First, we need to find the area of the overlapping region between the two circles. This can be done by finding the area of the sector of each circle that lies within the other circle and subtracting the area of the two smaller triangles formed by the intersection points.The area of a sector can be calculated using the formula:Asector=θ360∘·πr2where θ is the central angle of the sector in degrees and r is the radius of the circle.The central angle of each sector can be found by using the properties of overlapping circles. The angle is twice the inverse cosine of the ratio of the radius of each circle to the distance between their centers.Let P and Q be the points where the circles intersect. Then the distance PQ can be found using the Pythagorean theorem:PQ=2r2−d2where d is the distance between the centers of the circles.Substituting the values, we have:PQ=2202−d2Now we can find the central angle θ by using the inverse cosine function:θ=2·cos−1(rd)Substituting the values, we have:θ=2·cos−1(202202−d2)Now we can calculate the area of each sector using the formula mentioned earlier.Finally, the area of the swimming pool is the sum of the areas of the two sectors minus the areas of the two triangles:Aswimming&amp;nbsp;pool=2Asector−2Atrianglewhere Atriangle=12·PQ·rLet d be the distance between the centers of the circles, then d=2r.d=2·20d=40Now we can find PQ:PQ=2r2−d2PQ=2202−402PQ=2400−1600PQ=2−1200Since the value under the square root is negative, the circles do not intersect, which means the swimming pool does not exist.

Don Sumner · Accepted Answer

Result: 5309.73 square metersSolution:The area A of a circle is given by the formula A=πr2, where r is the radius of the circle.Given that each circle has a radius of 20m, we can calculate the area of each circle as follows:A1=π(202)A2=π(202)Since the circles overlap, we need to subtract the area of the overlapped region.The overlapped region consists of two identical circular segments. The area of a circular segment can be calculated using the formula:Asegment=θ360∘×πr2, where θ is the central angle of the segment.Since the circles pass through the center of the other, the central angle of each segment is 120 degrees (360 degrees divided by 3).The area of the overlapped region can be calculated as follows:Aoverlapped=2×Asegment=2×(120360×π(202))Finally, we can find the area of the swimming pool by subtracting the area of the overlapped region from the sum of the areas of the individual circles:Aswimming&amp;nbsp;pool=A1+A2−AoverlappedLet&#039;s calculate the values:A1=π(202)=π(400)=400πA2=π(202)=π(400)=400πAoverlapped=2×(120360×π(202))=23×π(400)=8003πAswimming&amp;nbsp;pool=400π+400π−8003π=800π−8003π=16003πNow, let&#039;s round off the answer to two decimal places:Aswimming&amp;nbsp;pool≈16003π≈5309.73Therefore, the area of the swimming pool is approximately 5309.73 square meters.

A swimming pool is constructed in the shape of two partially overlapping identical circles. Each of

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