SAT Math Multiple Choice Practice Question 546: Answer and Explanation
Note: Figure not drawn to scale.
A right circular cone is drawn above, with two circles centered at A on its base as shown. AB is the height of the cone, the measure of ∠ABC is 60°, and has a length of y. If bisects ∠ABC, which of the following gives the area of the smaller circle in terms of y ?
Correct Answer: E
E Plug in! There are two 30°-60°-90° triangles imbedded in this problem, so that is the best way to tackle this. Plug in for y, and go on from there. If you were to use 18 for y, the height of the cone would be 9. The base of the smaller triangle would be . That is also the radius of the circle, so square that number and get 27, and then multiply by π to get the area of the circle, which is 27π. This is the target. Plug your original value into the answer choices. If y = 18, the only answer that works out to 27π is E. Algebraically, the height is , and the base of the smaller triangle is (using the 30°-60°-90°). Square that and multiply by π, and you get E.