Question

in the diagram below, the width of the shaded reagion is exactly equal to the radius of the smaller circle (the circles are concentric) What part of the area of the larger circle is the area of the shaded region?

Answer 1

you mean what part from the center?

Answer 2

\[A_{\text {circle}}=\pi r^2\]

Answer 3

i think it means the area of only the ring

Answer 4

the ring is a difference of circles

Answer 5

\[A_{\text {ring}}=\pi R^2-\pi r^2\]\[R=2r\]

Answer 6

if we take the radius of the smaller circle 'r' then the radius of the bigger one would be '2r'
are the shaded are = pi*(2r)^2 - pi*r^2

Answer 7

area of the shaded are = pi*(2r)^2 - pi*r^2

Answer 8

so we only need the radius of the smaller circle r

Answer 9

the question asks for
\[\frac{A_{\text{ring}}}{A_{\text {large circle}}}\]

Answer 10

ok how do we find the radius?

Answer 11

the radius of the large circle is R=2r

Answer 12

so it would be like
\[(\pi (2r)^2-\pi r^2)/(\pi (2r)^2)\]= 3/4

Answer 13

i think so

Answer 14

aright thinks

Answer 15

yeah that is correct

Answer 16

it even looks right.