Question

Describe the surface whose equation in cylindrical coordinates is z = 5r. SOLUTION The equation says that the z-value of each point on the surface is the same as 5r, the distance from the point to the z-axis. Because θ doesn't appear, it can vary. So any horizontal trace in the plane z = k (k > 0) is a circle of radius r = Incorrect: Your answer is incorrect. . These traces suggest that the surface is a cone. This prediction can be confirme

Answer 1

Answer and explanation:

z = 5r represents cone

in the plane z = k (k > 0)

k=5r

`\\\mathrm{=>r=(k)/(5)}\\`

The equation says that the z-value of each point on the surface is the same as five times r,

the distance from the point to the z-axis. Because θ doesn't appear, it can vary. So any horizontal trace in the plane z = k (k > 0) is a circle of radius

`\\\mathrm{r=(k)/(5)}\\`