The following equations i)-viii) represent curves or surfaces. Match each of the

Question

The following equations i)-viii) represent curves or surfaces. Match each of the equations with one of the geometric a)-g). If none of a)-g) applies, write none. (Note rho, phi, theta are spherical coordinates; r, theta, z are cylindrical coordinates.)

i) r =2, 0 <= z <= 10

ii) x = t, y = 2t, z = 3t, 0 <= t <= 10

iii) x = t^2, y = 2*t^2, z = 3*t^2, 0 <= t <= 10

iv) z = 10, 0 <= r <= 10

v) rho = 1/ cos(phi), 0 <= phi <= pi/3

vi) rho = cos(phi), theta = pi/4, 0 <= phi <= pi/3

vii) phi = pi/4, 0 <= rho <= 10

viii) z = r^2, theta = pi/4, 0 <= r <= 10

a) Part of a line through the origin

b) Part of a parabola through the origin

c) Line or curve through (x,y,z) = (0,0,1) in a horizontal plane

d) Line or curve through (x,y,z) = (0,0,1) in a vertical plane

e) Disc

f) Part of a cone

g) Part of a cylinder

Explanation / Answer

1 - g

2 - a

3 - a

4 - e

5 - e

6 - d

7 - f

8 - b

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