Question

The clubhouse has a water tank from which hikers fill their water jugs before walking the trail. The tank is a 5-gallon cylindrical container with a height of 2 feet and a radius of 4 inches. Alex fills his 1-gallon jug from the clubhouse tank before going on a hike. If the 5-gallon tank was full, what was the height of the water in the tank after Alex filled the 1-gallon jug?(A) 1.6 inches(B) 4.8 inches(C) 19.2 inches(D) 964.6 inches

Answer 1

Answer: 19.2 inches would be the most reasonable answer, since the first two is too small, and the last answer would be too tall.

if there was 2 feet of water, it would be 24 inches full. taking 1 gallon out, wouldn't make the difference to make it go up or down much.

Answer 2

c) 19.2 inches

Explanation:

Height of water when full = 2 feet = 24 inches

Radius of cylinder = 4 inches

Volume of tank = 5 gallon

Gallon per inch height of tank =
`(5)/(24)`

Inch per gallon of height =
`(24)/(5)`

So, when 1 gallon is removed

`24-1* (24)/(5)=(96)/(5)=19.2\ inches`

∴ Height of the water in the tank after Alex filled the 1 gallon jug is 19.2 inches.

or

Volume of cylinder after 1 gallon was removed

`\pi r^2h=4* 231\\\Rightarrow h=(4* 231)/(\pi 4^2)\\\Rightarrow h=18.38\ inches`

∴Height of the water in the tank after Alex filled the 1 gallon jug is 18.38 inches

The different height arises due to the thickness of the rank which is not given.

The first method is more accurate