Cracking The SAT Premium

shape (pun entirely intended)!

Let’s look at an example:

15.A    sphere  has a   volume  of  36π.    What    is  the surface area    of  the sphere? (The    surface area    of

a   sphere  is  given   by  the formula A   =   4πr^2 .)

A) 3π

B) 9π

C) 27π

D) 36π

Here’s How to Crack It

Start by writing down the formula for volume of a sphere from the beginning of the chapter: V = πr. Put

what you know into the equation: 36π = πr^3 . From this you can solve for r. Divide both sides by π to get

36 = r^3 . Multiply both sides by 3 to clear the fraction: 36(3) = 4r^3 . Note we left 36 as 36, because the

next step is to divide both sides by 4, and 36 divided by 4 is 9, so 9(3) = r^3 or 27 = r^3 . Take the cube root

of both sides to get r = 3. Now that you have the radius, use the formula provided to find the surface area:

A = 4π(3)^2 , which comes out to 36π, which is (D).

Ballparking

You may be thinking, “Wait a second, isn’t there an easier way?” By now, you should know that of course
there is, and we’re going to show you. On many SAT geometry problems, you won’t have to calculate an
exact answer. Instead, you can estimate an answer choice. We call this Ballparking, a strategy we
discussed earlier in this book.

Pictures

Unless  otherwise   stated,

any diagram that    is  provided

is  drawn   to  scale.

Ballparking is extremely useful on SAT geometry problems. At the very least, it will help you avoid
careless mistakes by immediately eliminating answers that could not possibly be correct. In many
problems, Ballparking will allow you to find the answer without even working out the problem at all.

Rocket  Science?

The SAT is  a   goofy   college

admissions  test,   not an

exercise    in  precision.