The radius of cylinder C is 5 inches, and the height of cylinder C is 5 inches. What is the greatest possible straight line distance, in inches, between any two points on a cylinder C?
A. 52
B. 53
C. 55
D. 10
E. 15
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A. 52
B. 53
C. 55
D. 10
E. 15
[Reveal] Spoiler:
The greatest possible straight line distance, in inches, between any two points on a cylinder C is line segment AB.
Drawing the cylinder shows that this problem is actually a 2 dimensional problem in a 3D disguise - finding the hypotenuse of a right triangle: AB is the hypotenuse of right triangle ABC, whose legs are AC=5 - the height of the cylinder, and BC=5+5=10 - the diameter of the cylinder.
Use the Pythagorean Theorem to find AB.
--> (AB)2 = 52 + 102
--> (AB)2 = 125
--> AB = 125 = 55
Attachment:
T8289.png
Drawing the cylinder shows that this problem is actually a 2 dimensional problem in a 3D disguise - finding the hypotenuse of a right triangle: AB is the hypotenuse of right triangle ABC, whose legs are AC=5 - the height of the cylinder, and BC=5+5=10 - the diameter of the cylinder.
Use the Pythagorean Theorem to find AB.
--> (AB)2 = 52 + 102
--> (AB)2 = 125
--> AB = 125 = 55