Question

In space, which description fits the locus points 3 cm from line AB

Answer 1

Possible answers are
A. an open cylinder of diameter 6 cm
B. an open cylinder of radius 3 cm and two hemispheres of diameter 6 cm each
C. an open cylinder of radius 3 cm and height 6 cm
D. an open cylinder of diameter 6 cm and two spheres of radius 3 cm each

Answer 2

well on the 2D plane, the locus of all points that are equally distant away from a given point would be a circle

Answer 3

now imagine pulling that circle out of the plane in a straight line

the 3D figure you would get would be a cylinder

Answer 4

@jim_thompson5910 in your mind would the cylinder have a diameter of 6 or would you say it has a radius of 3 and 2 hemispheres

Answer 5

and 2 hemispheres of 6

Answer 6

here is the 2D version of what I'm describing

it's just a circle centered at some point



any point on that circle will be equally distant to the center (compared to any other point)

Answer 7

So no hemisphere is involved

Answer 8

now imagine pulling that figure out of the page to get this

Answer 9

@jim_thompson5910 I get it!! Thank you so much!

Answer 10

if line AB is in the direct center, then we would get this

Answer 11

any point found on the outside of the cylinder will be equally distant away from some other point found on the outside of the cylinder

Answer 12

equally distant from AB

Answer 13

The base of that cylinder is not a hemisphere is it?

Answer 14

there's a cut off, but imagine this cylinder is going off forever in both directions

Answer 15

like a beam of light or something

Answer 16

no it's just an open cylinder and that's it

no hemispherical caps or anything