Problem Solving

Plz help to interpret the wording from OG Review.

A closed cylindrical tank contains 36Ï€ cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 2 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

Does the OG says that 36Ï€ equals the full or the half capacity of the tank?

Based on the OG explanation, OG takes 36Ï€ as a full capacity of the tank, which contradicts the description. To my understanding,

cylindrical tank contains 36Ï€ cubic feet of water and is filled to half its capacity

36Ï€ is a half, and full capacity should be 72Ï€.

Please, explain how to read the right meaning.

Thank you.

OG solution

water level
radius = half the height
Using the information about the volume of water
in the upright cylinder, solve for this radius to
determine the height of the water when the
cylinder is on its side.
V = πr2h
36π = πr2h
36= r2(4)
9 = r2
3 = r
volume =(k)(radius2)(height)
known volume of water is 36Ï€
substitute 4 for h; divide both
sides by π solve for r
radius = height of the water
in the cylinder on its side [/b]

Your analysis is correct. There is an error in the question in that version of the Official Guide. The height when then tank is filled half way should be 4 feet.

Here is a link to the official errata.

https://media.wiley.com/product_ancillar ... Errata.pdf

AndreiGMAT wrote: To my understanding,

cylindrical tank contains 36Ï€ cubic feet of water and is filled to half its capacity

36Ï€ is a half, and full capacity should be 72Ï€.

Please, explain how to read the right meaning.

You are correct! The GMAC flubbed this one; it happens from time to time.