Explanation for Question 34 From the Math (Calc) Section on the Official Sat Practice Test 3
Now looking at number 34, we have a circle with the center. 2 Oh. So we'll draw out our circle with central angle a O B. 3 So we've got an angle right here, AOB and this angle measures five PI 4 over four radians. Um, 5 and so we want to know the area of the sector, 6 um, formed by the central angle is what fraction of the area 7 of the circle. And so essentially what we need to see here is that 8 the area of the sector as a fraction of the circle is the same 9 as what fraction of the circle this angle is. 10 Right? And so we know we have five PI over four radians as 11 our percentage or our angle of the circle. 12 And so when you find a percentage, you're really doing the part over the 13 whole. In this case, the five PI over four is the parts that we 14 have. 15 And the whole angle of a circle is 360 degrees, 16 which is also two PI. So what we're really doing here is we're 17 taking, um, this, this fraction here. 18 Oops. Um, 19 where did it go right here? 20 We're taking this fraction here, five PI over 4, 5, 5 over four. 21 And we're dividing it by two PI, right? 22 Which is the same thing as multiplying times one over two PI, 23 we'll see that the pies they can't sell out immediately. 24 And if we multiply across, we get five over eight is our answer. 25 And so just to reiterate, this is really taking the, 26 uh, the angle that we have and dividing it by the total angle measure 27 of a circle.