Question

(Note: In this problem, a "cylinder means the can-shaped figure that we used to recognize as a cylinder. not the cylinder defined in the sense as in Section 12.6.) Problem: Three circular cylinders, each with radius v3, are standing tangent to one another on the plane $2. as shown in the figure above. Let P, Q, and R denote the centers of the upper circular bases of the shortest cylinder, the next shortest cylinder, and the tallest cylinder, respec- tively. Suppose the following: AQPR is a isosceles triangle * The measure of the angle between plane QPR and plane Ω is 60° * The hcights of the thrcc cylinders are 8, a, and b, with 8<a<b Find the value of ab. 1. As stated in the problem, AQPR is an isosceles triangle. Among PQ, QR, and RP, can you tell which ones are equal in length? 2. Let Qu·Po, and Ro be the ccnters of the bottom bases of the thrcc respective cylinders. What kind of triangle is △Q0PoRo? 3. You may have noticed by now that a good way to solve this problem may be to look at each point as a point in R3. Let Ω be the :ry-plane so that /NQoPoRo is a triangle on the ry-plane Label Qu, Pi, and Ro as points on the ry-plane with suitable coordinates. (What would be a good way to do this? Should you label one of the points as (0, 0,0)? Which one would that be?) Continued on the nert page)

Answer 1

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