Cylindrical coordinates? hi,
i am having problems with a homework question,
i am asked to sketch the solid by the given inequalities.
0 < = theta < = pi/2 and r < = z < = 2
how do i find r?
if possible guide me to the answer instead of giving it to me. i need to know this stuff.
in advance for any .

tells you that and .

Recalling that in cylindrical coordinates, , we then know that , and so we're confined to the first octant (where each of are non-negative).

The upper limit of tells us that the region is bounded above by the plane , which is parallel to the - plane.

Meanwhile, the lower limit of can be visualized by first squaring both sides:



If you're not already familiar with what this equation represents, we can approach it piecemeal. At one extreme, when , we have , so the region has a "vertex" at the origin.

When , we have the Cartesian equation , which corresponds to a circle of radius 2. Similarly, if we consider values of between 0 and 2, we end up with circles of increasing radii. Stacking these circles onto one another, we get a cone.

More specifically, the region is the part of the cone between the - plane and the plane restricted to the first octant.

(Image of region attached)