If you had a pizza with crust thickness 'a' and radius 'z', what's the volume of the pizza?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

Which is the correct shadow of the bird?

Below toothpicks/matchsticks indicate the group of fishes moving from west to east direction. Can you make them move from east to west by just moving three toothpicks/matchsticks?

If two fifty-foot ropes are suspended from a forty-foot ceiling that is twenty feet apart, how much rope will you be able to steal if you have a knife?

At a party, there are five people and a whole round cake lying at the centre of the table. Only four people will make a cut and take their piece and the last one will get the remaining piece on the table. How can they make sure that everyone gets a 1/5th of the piece?

A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff and got these alibis: The Wife said she was sleeping. The Cook was cooking breakfast. The Gardener was picking vegetables. The Maid was getting the mail. The Butler was cleaning the closet. The police instantly arrested the murderer. Who did it and how did they know?

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

Can you replace the question mark with the correct number in the below table sequence?

A boy purchased a book from a bookkeeper and gave him $100.
The cost of the book is $50 but the bookkeeper has no change, so he gets the change from the next shop and returns the boy his $50.

After some time the next shopkeeper came with the $100 note and told the bookkeeper that the note was a fraud, so he took the money back.

How much loss did the bookkeeper face?