Explanation for Question 13 From the Math (No Calc) Section on the 2019 October Sat
Now for question number 13, we are talking about the volume of a right 2 circular cone, which looks a little, 3 something like this. And so in order 4 to do this question, we need to know the formula for the volume of 5 a cone. And the volume of a cone is equal to PI 6 R squared times height divided by three. 7 It's really just the equation for volume of a cylinder. 8 And then you divide that by three. And we're told that the volume is 9 one over three PI, right? 10 And that the height is nine feet. 11 So that's equal to PI R squared times nine we'll plug in nine for 12 the height. Divide that by three. And then a question is asking us for 13 the radius. So now we're just going to take this equation that I've written 14 here and solve for R. Now, 15 the first thing that we can think about doing is simplifying this nine and 16 the three, right? 17 Because nine divided by three, that is just three. 18 So I can rewrite this equation. As one, 19 over three PI is equal to three PI R squared. 20 And now we can see that there's a pie in the, in the numerator, 21 both sides. So these pies can cancel simply leaving me 22 with a one over three. Nope. 23 I actually canceled the three. They're leaving us with a one over three is 24 equal to three R squared. So now to get our alone, 25 to isolate our, I need to first remove this positive three and says it's 26 three times R squared. I can do that by dividing both sides by three. 27 So if I divide both sides by three, that gives us a one o...