How to figure out volume of 3d pizza slice shape

me and a friend are doing a math project. we need to get a box and change the surface area, but keep the volume the same. we decided to make a regular pizza box into the shape of a pizza slice and then you could stack the pieces on top of each other (stupid idea, I know. but we don't actually have to do it) so I need to know how'd you figure out the volume for such a weird shape.

The area of a circle is pi r^2 where r is the radius of the circle

If a pizza with radius r is cut into, say, 8 slices, the area of each slice is (pi r^2)/8

The volume of a slice is t*(pi r^2)/8 where t is the thickness of the slice.

If you stack all 8 slices the total volume is t*(pi r^2)

It isn't necessarily valid to hold the volume constant. If that's part of the assignment, fine, but it isn't realistic. A pizza is round, with some non-constant height because the crust is usually taller than the rest of the pizza, and the pizza surface is somewhat uneven. The pizza box is typically square, with a side length that's equal to or just slightly greater than the diameter of the pizza, so there is some wasted space in each corner of the square box. Also, the box has to be tall enough that the tallest part of the pizza (usually the crust) can fit within it, so there is more wasted space above the lower portions of the pizza.

If you cut the pizza into slices, stack them, and adjust the shape of the box accordingly, there will typically be a different amount of total wasted space, and therefore a different total box volume than when the box was shaped like a traditional pizza box.

if you want to figure the volume of that 3d pizza, why you not fill your bucket with water until it is full, then put the pizza into the bucket. some water will spill out. then the volume of the spilled water is the volume of 3d pizza.