Answer:
"Depth (D) is inversely proportional to the amount of water (A) in a tank" seems incorrect. Water volume should be directly proportional to the water depth. Perhaps the term Depth is meant to be the distance from the top of the tank to the water level? Answers are provided for this revised definition of "depth."
(a) D = 140 cm
(b) Volume = 140 L
Explanation:
Depth = 1/Amount or D = r/A [2) Depth (D) is inversely proportional to the amount of water (A) in a tank. ] r is a factor that converts liters to cm. We aren't old the value of r, but will calculate it from the sentence:
"When Ali took 200 liters of water, the depth is 350 cm."
Knowing this, we can calculate a value of r that should have units of cm*liter (the conversion that tells us how liters relates to cm, the water height in the tank.
D = r/A
(350 cm) = r/(200 L)
r = 70,000
D = (70,000 cm*L)/A
Try this for 200L:
D = (70,000 cm*L)/(200L)
D = 350cm Correct
a) What is the depth of the water if he takes 500 liters.
D = (70,000 cm*L)/(500L)
D = 140 cm Incorrect, unless we assume it is the distance from the top of the tank to the water.
If one adds water to a tank, one would expect the depth to increase, not decrease. So either this is an unusual tank, or the description "inversely proportional" is incorrect. It7 would seem the relationship should be directly proportional. not inversely, as stated in the problem. But let's do the second part, just in case the definition of depth is from the top of the tank to the water surface.
(b)
D = (70,000 cm*L)/A
500cm = (70,000 cm*L)/A
A = 140 L