Solids

Read the following SAT test question and then select the correct answer.

The Knowsys method requires you to read each math question carefully and identify the bottom line.  You must also assess your options to find the best way to attack the problem, solve it, and loop back to make sure that you solved for the bottom line.

A right circular cylinder has height 6 and volume 54π. What is the circumference of its base?

Make a note of the fact that you are solving for the circumference of the base by writing C  = ? under the problem.  You should know that C = 2πr, and based on that you should realize that this problem will require more than one step.  You cannot solve for the circumference of the base without knowing the radius of the base circle.  You do know the volume of the cylinder, so you can use that information to find out more about the base circle.  You should have the formula for the volume of a cylinder memorized: Volume = πr²h. Plug in the values you already know to solve for the radius.

V = πr²h
54π = πr²6   (divide each side by 6π)
9 = r²    (take the square root of both sides)
3 = r

You now have the information that you need for the circumference formula.  Be careful not to look down at your answers yet, because even though you solved part of the problem, you have not yet found the bottom line.

C = 2πr
C = 2π3
C = 6π

Now that you have an answer, match your answer to the answer choices.

(A) 2π
(B) 3π
(C) 6π
(D) 9π
(E) 18π

The correct answer is (C).


On sat.collegeboard.org, 41% of the responses were correct.

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