According to a popular, but untrue, urban legend, oceanographers have discovered images of giant pyramids made of crystal-like substances deep in the ocean. Suppose one of these imaginary pyramids has the dimensions shown at the right.

The volume V of a pyramid is 1/3 Bh where B is the area of the base and h is the height of the pyramid.

Part A
Find an equation that represents V in terms of x. Then find x in terms of V. Write your equation for x in
rational exponent form, and rationalize denominators where necessary. Show your work

Part B
Suppose a pyramid has a volume of 2,000,000 m^3. What is the height x of the pyramid? Show your
work

Part C
Suppose the urban legend were true, and a contractor could be hired to raise one of these pyramids and bring it to the surface of the ocean The estimated cost of the operation c(x) is $200,000 per meter of pyramid height with an additional cost a(v) of $300 per cubic meter of pyramid volume. What is an equation that represents the total retrieval cost t for a pyramid of any volume with these proportions in terms of x? How much would it cost to excavate this pyramid? Show your work.