<p>Hey there, could someone please tell me why the answer for question 12 on page 371 in the Official SAT Study guide is 3:7?</p>
<p>"In the figure above, the four circles have the same center and their radii are 1,2,3, and 4, respectively. What is the ration of the area of the small shaded ring to the area of the large shaded ring?"</p>
<p>The small shaded ring is the second circle, the large shaded ring is the last one.</p>
<p>Thanks in advance! :)</p>
<p>The question isn’t asking for the ratio of the areas of the circles. It’s asking for the ratio of the areas of the rings, which can be found by subtracting the area of the circle whose perimeter forms the inner boundary of the ring from the area of the circle whose perimeter forms the outer boundary of the ring:</p>
<p>Small shaded ring:
pi<em>2</em>2 - pi<em>1</em>1 = 4pi - pi = 3pi</p>
<p>Large shaded ring:
pi<em>4</em>4 - pi<em>3</em>3 = 16pi - 9pi = 7pi</p>
<p>Ratio: 3pi:7pi = 3:7</p>
<p>Thanks for the answer, purplepotato (is their a possibility that we’re related some way? :P)!</p>
<p>Turns out this whole time I was doing pi<em>4</em>4 - pi<em>3</em>3 - pi<em>2</em>2 - pi<em>1</em>1 for some reason -_- It’s the stupid mistakes like that which I have problems with.</p>
<p>can somebody help me with this problem?</p>