Explanation for Question 17 From the Math (Calc) Section on the Official Sat Practice Test 10
Now for number 17, the question says that the volume of a sphere is 2 given by this particular formula, 3 this formula right here, where R is the radius. 4 Um, and then it says which of the following gives the radius in terms 5 of the volume of the sphere. And so you can see that they want 6 us to give the radius. They want us to solve for radius. 7 When they say give radius, they mean solve for radius. 8 And then when they say in terms of the volume of the sphere of 9 this phrase, in terms of simply means that they want to have a V 10 for volume in the equation, 11 you can see that there's a V in each of these equations. 12 So that means they're all in terms of volume. 13 So what we're going to do is we're going to take this original equation. 14 We're just going to shuffle things around. 15 So that R is on its own because right now our is surrounded by 16 a lot of things. And the first thing I'll get rid of is that 17 fraction three over four, to get rid of a fraction, 18 you can multiply by its reciprocal. So these fours will cancel 19 out. These threes will cancel out and I'll be left with three. 20 Over four volume is equal to PI R cubed. 21 Now to get rid of that PI I can divide by PI divide everything 22 by PI. These pies will cancel. 23 And this four goes into the denominator with the pie. 24 So I can write a three V over four PI is equal to R 25 cubed and now to solve for RQ or just for R rather, 26 I need to take the cube root of those sides because the cube root 27 will cancel out that art to the third and just make it R that 28 means that the cube root of three V over four PI is equal to 29 R. And we see that right here and answer choice D.