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MATH / In the diagram, the three concentric circles have radii of 4, 6, and 7. Three regions are labeled X, Y, or Z below. Of these three regions, what is the difference between the area …

Problem

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

problem

In the diagram, the three concentric circles have radii of 4,4, 6,6, and 7.7. Three regions are labeled X,X, Y,Y, or ZZ below. Of these three regions, what is the difference between the area of the region with the greatest area and the area of the region with the smallest area? Express your answer in exact form. [asy] import graph; filldraw(circle((0,0),7), lightgray, black+linewidth(1)); filldraw(circle((0,0),6), gray, black+linewidth(1)); filldraw(circle((0,0),4), white, black+linewidth(1)); dot((0,0)); label("XX",(2,0)); label("YY",(5,0)); label("ZZ",(6.5,0)); [/asy]
Plain-text mathematical notation (without MathML)
In the diagram, the three concentric circles have radii of 4, 6, and 7. Three regions are labeled X, Y, or Z below. Of these three regions, what is the difference between the area of the region with the greatest area and the area of the region with the smallest area? Express your answer in exact form.

[asy]
import graph;
filldraw(circle((0,0),7), lightgray, black+linewidth(1));
filldraw(circle((0,0),6), gray, black+linewidth(1));
filldraw(circle((0,0),4), white, black+linewidth(1));
dot((0,0));
label("X",(2,0));
label("Y",(5,0));
label("Z",(6.5,0));
[/asy]
Original LaTeX notation
In the diagram, the three concentric circles have radii of $4,$ $6,$ and $7.$ Three regions are labeled $X,$ $Y,$ or $Z$ below. Of these three regions, what is the difference between the area of the region with the greatest area and the area of the region with the smallest area? Express your answer in exact form.

[asy]
import graph;
filldraw(circle((0,0),7), lightgray, black+linewidth(1));
filldraw(circle((0,0),6), gray, black+linewidth(1));
filldraw(circle((0,0),4), white, black+linewidth(1));
dot((0,0));
label("$X$",(2,0));
label("$Y$",(5,0));
label("$Z$",(6.5,0));
[/asy]

level

Level 5

type

Prealgebra

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Source and history

task_id
5b9d1fae-c6c7-59de-b78d-fbc7befd978e
task_key
prealgebra--test--5b9d1fae-c6c7-59de-b78d-fbc7befd978e
task_revision_id
1
config / split
prealgebra / test

Official source

initial import