Hello, numberonenacho!

A region in space when viewed from 3 different views,

looks like a circle, looks like a square and looks like a triangle.

Describe this object in words or pictures,

and then use multiple integration to determine its volume.

Consider a right circular cylinder with diameter $\displaystyle a$ and height $\displaystyle a$.

Stand it on one of its circular bases.

Looking down, we see a circle.

Looking from the side, we see a square . . . like this: Code:

*---------------*
| |
| |
| |
a | |
| |
| |
| |
*---------------*
a

Make two diagonal cuts as shown below. Code:

* - - - * - - - *
: / \ :
: / \ :
: / \ :
: / \ :
: / \ :
: / \ :
:/ \:
*---------------*

Looking down, we see a circle.

Looking from the right (or left), we see a square.

Looking from the front, we see a triangle.