Explanation for Question 33 From the Math (Calc) Section on the Official Sat Practice Test 6
Question 33 asks us a laboratory supply company produces, 2 graduated cylinders each with an internal radius of two inches and an internal 3 height between 7.75 inches and eight inches. 4 What is one possible volume around it to the nearest cubic inch of a 5 graduated cylinder produced by this company? 6 Okay. So let's think about what we have here and let's first 7 draw a picture. So we've got a cylinder and we know 8 for sure that the internal radius is two inches. 9 So let's label this R and we have R is equal to two inches 10 and the height here, we have a range. 11 So the height has to be between eight inches and 7.75 12 inches. So something that I noticed immediately is we just need one possible 13 volume so we can pick any arbitrary point for the height in 14 between 7.7, five and eight. 15 And that should work. And let me actually write this as just the 16 symbols, because we don't know for sure if it's equal to it. 17 Doesn't explicitly say that since between 7.75 and eight. 18 So just to be safe, let's write it like this. 19 So let's pick our height, arbitrarily a 7.80 inches, 20 sorry, have H S equal to 7.80 inches and R is equal to two 21 inches. We're trying to find the volume. 22 So we need to know the volume of a cylinder and that 23 expression is going to be PI R squared H so 24 we have R is equal to two inches squared times 25 7.80. 26 So we have four PI times 7.80, 27 and let's solve this out really quick. We have four times 3.1415 28 or so times 7.80 we're left with V 29 is equal to 98.015 30 cubic, excuse me. That should be cubic inches. 31 So inches cute. But remember we have to bubble in 32 the possible volume rounded to the nearest cubic inch. 33 So for us, that's going to be 98. We can bubble in V is 34 equal to 98 cubic inches.