SAT Example (the Mathematics Section)
작성자
CLI 아카데미
작성일
2018-12-31 12:28
조회
874
Mathemathics Section: Multiple choice question
Two spheres, one with radius 7 and one with radius 4, are tangent to each other. If P is any point on one sphere and Q is any point on the other sphere, what is the maximum possible length of PQ ?
(A) 7
(B) 11
(C) 14
(D) 18
(E) 22
Answer & Explanation
Choice (E) is correct. The maximum possible length of ![line P Q]()
is equal to the sum of the diameters of the two spheres, which is ![(2 times 4) + (2 times 7) = 22]()
as can be seen in the figure below.
Choice (A) is not correct. The maximum possible length of ![line P Q]()
is greater than ![7]()
, as can be seen in the figure above. This choice is the radius of the larger sphere. The correct answer is the sum of the diameters of the two spheres, which is ![22]()
.
Choice (B) is not correct. The maximum possible length of ![line P Q]()
is greater than ![11]()
, as can be seen in the figure above. This choice is the sum of the radii of the two spheres. The correct answer is the sum of the diameters of the two spheres, which is ![22]()
.
Choice (C) is not correct. The maximum possible length of ![line P Q]()
is greater than ![14]()
, as can be seen in the figure above. This choice is the diameter of the larger sphere. The correct answer is the sum of the diameters of the two spheres, which is ![22]()
.
Choice (D) is not correct. The maximum possible length of ![line P Q]()
is greater than ![18]()
, as can be seen in the figure above. This choice is the sum of the radius of the smaller sphere and the diameter of the larger sphere. The correct answer is the sum of the diameters of the two spheres, which is ![22]()
.
(practice question from Collegeborad)