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MATH / Four semi-circles are shown with AB:BC:CD=1:2:3. What is the ratio of the shaded area to the unshaded area in the semi circle with diameter AD? Express your answer as a common frac…

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Answer published by the source. Consult the official source to check your work against its answer.

problem

Four semi-circles are shown with AB:BC:CD=1:2:3AB:BC:CD = 1:2:3. What is the ratio of the shaded area to the unshaded area in the semi circle with diameter ADAD? Express your answer as a common fraction. [asy] import olympiad; import geometry; size(150); defaultpen(linewidth(0.8)); filldraw(arc((6,0),6,0,180)--cycle); filldraw(arc((3,0),3,0,180)--cycle,fillpen=white); filldraw(arc((8,0),2,0,180)--cycle,fillpen=white); filldraw(arc((11,0),1,0,180)--cycle,fillpen=white); label("AA",(12,0),S); label("BB",(10,0),S); label("CC",(6,0),S); label("DD",(0,0),S); [/asy]
Plain-text mathematical notation (without MathML)
Four semi-circles are shown with AB:BC:CD=1:2:3. What is the ratio of the shaded area to the unshaded area in the semi circle with diameter AD? Express your answer as a common fraction. [asy]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8));
filldraw(arc((6,0),6,0,180)--cycle);
filldraw(arc((3,0),3,0,180)--cycle,fillpen=white); filldraw(arc((8,0),2,0,180)--cycle,fillpen=white); filldraw(arc((11,0),1,0,180)--cycle,fillpen=white);
label("A",(12,0),S); label("B",(10,0),S); label("C",(6,0),S); label("D",(0,0),S);
[/asy]
Original LaTeX notation
Four semi-circles are shown with $AB:BC:CD = 1:2:3$. What is the ratio of the shaded area to the unshaded area in the semi circle with diameter $AD$? Express your answer as a common fraction. [asy]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8));
filldraw(arc((6,0),6,0,180)--cycle);
filldraw(arc((3,0),3,0,180)--cycle,fillpen=white); filldraw(arc((8,0),2,0,180)--cycle,fillpen=white); filldraw(arc((11,0),1,0,180)--cycle,fillpen=white);
label("$A$",(12,0),S); label("$B$",(10,0),S); label("$C$",(6,0),S); label("$D$",(0,0),S);
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
9339b6ff-cac1-5f95-94fb-e4d87fde0db8
task_key
geometry--test--9339b6ff-cac1-5f95-94fb-e4d87fde0db8
task_revision_id
1
config / split
geometry / test

Official source

initial import