Explanation for Question 20 From the Math (No Calc) Section on the Official Sat Practice Test 6
Question 20 asks us points a and B lie on a circle with radius. 2 One, an arc AB has length PI over three. 3 What fraction of the circumference of the circle is the length of arc a 4 B. So to start, 5 we're going to draw just a really simple circle and visualize what's going on 6 here. So let's say that another, 7 this is all approximate, that this is point a, 8 and this is point B and they 9 are on a circle with a radius of one. 10 So this point right here is the center. So that radius is one and 11 one. And the length of this is PI over three. 12 It's asking what fraction of the circumference of the circle is the length of 13 arc AB. Now we know that circumference, 14 so I'll just write C is equal to PI D and 15 D is equal to two R. 16 So we have C is equal to PI. 17 Times two are knowing that our R is one. 18 We get that their circumference is equal to two PI. 19 So now we find, we're trying to find the fraction of the circumference of 20 the circle. What fraction of the circumference of that circle is the length of 21 arc AB. So let's find the length of a B 22 over C and that's going to be equal to PI 23 over three divided by two PI. 24 So we can also picture this as 25 PI over three times two PI. 26 So the pies are going to cancel out and we will get one over 27 three times two, which is six. So we get that one sixth is the 28 fraction that we're looking for.