Problem 65 - Introductory and Intermediate Algebra for College Students 4th

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 was used in the three-month period?

Step-by-Step Solution

Answer

To find the volume of water used, we first need to calculate the initial and remaining volumes of the water in the reservoir, and then subtract the remaining volume from the initial volume. This difference will indicate how much water was used during the three-month period of no rain.

Step 1: Calculate the initial volume

The reservoir is in the shape of a rectangular solid, so the volume can be calculated by the formula: \(Volume = length * width * height\). Considering the dimensions of the reservoir are 50 yards by 30 yards, and a vertical height of 20 yards, the total volume when the reservoir was full can be calculated as:\(Volume_{initial} = 50yards * 30yards * 20yards\)

Step 2: Calculate the remaining volume

At the end of the three-month period, the height of the water was 6 yards while the length and the width remained the same. So, the remaining volume of the reservoir can be calculated as: \(Volume_{remaining} = 50yards * 30yards * 6yards\)

Step 3: Determine the volume of water used

The volume of water used during the three months period can be calculated as the difference between the initial volume and the remaining volume: \(Volume_{used} = Volume_{initial} - Volume_{remaining}\)