Week 20, Problem 3 By: Fabian S. Week 20, Problem 3 By: Fabian S.

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Presentation transcript:

Week 20, Problem 3 By: Fabian S. Week 20, Problem 3 By: Fabian S.

The Problem…. Four concentric circles are drawn with radii of 1,3,5, and 7. The inner circle is painted with black, the ring around it is white, the next ring is black, and the outer ring is white. What is the ratio of the black area to the white area? Express your answer as a common Fraction.

Important things to remember…… What I need to do to solve this problem is to find the area of each black or white ring, but here's the thing, I only have the radios of each black and white ring. So now I need to use the formula, Area= pie * radios squared in order for me to be able to solve the problem

My work… So the first white outer ring has a radios of 7. So now I plug in 7 as the radios and I do my work… A= 3.14*7squared= 154 The next black ring has a radios of 5 so I do the same thing, plug in 5 as the radios and then do my work… A= 3.14*5squared= 79 The next white ring has a radios of 3 so I do my work and plug in 3 as the radios A= 3.14*3Squared= 28 And the final black ring has a radios of 1 so I do what I showed above A= 3.14*1squared= 3 * Note: 3.14 Means pie only that I simplified it to the first three digits

More of my work… So now I got my answers of what the rings equal, W=154, B=79, W=28, and B=3 and now I take those answers and I subtract them by the number following in the row For Ex. W=154-79= 75 B=79-28= 51 W=28-3= 25 B=3 3 Now I take the answers I got after I subtracted them and then add up all the black and white groups separate so the answers to the black rings get added up together and the answers to the white rings get added up together. Black Rings: 51+3=54 White rings: 75+25=100

The final steps……. So now the last thing I have to do is put the ratio as a common fraction which will be 54/100 But that’s not it I could still simplify that so I would divide it by 2 so it could be simplified. It will end up being 27/50 for my final answer.

My final answer….. 27/50

Any questions? I will be happy to answer, but remember I'm Fabian so yeah, ill try to answer as best as I can