help? Thanks (:

Question

A water reservoir is shaped like a rectangular solid with a base that is 50 yards by 30 yards, and a vertical height of 20 yards. At the start of a three-month period of no rain, the reservoir was completely full. At the end of this period the height of the water was down to 6 yards. How much water (in gallons) was used in the three-month period? (1 cubic foot = 7.48052 gallons).

Answer 1

Hello Tatiana

 

The volume of the reservoir, the rectangular solid is LxWxH

50 x 30 x 20 = 30000 cubic yards

 

At the end of the 3 months, the volume was

50 x 30 x 6 = 9000 cubic yards  since the height of the water was down to 6 yards from the original 20

 

So the difference in the volume of water was

30000 - 9000 = 21000 cubic yards

 

We need to convert this into gallons of water.  We are given the relationship between a gallon of water and cubic feet but we have cubic yards, so first we much convert the 21000 cubic yards to cubic feet.

 

There are 27 cubic feet in a cubic yard

21000 cubic yards x 27 cubic feet/cubic yard = 567000 cubic feet

 

Now 1 cubic foot = 7.48052 gallons

 

567000 cubic feet x 7.48052 gallons/cubic foot = 4,241,455 gallons.