Question

Not sure on how to do this. Could really use some help. The numbers you're using are from the 1st image with the 300 150 and 200. I sent a second one with the numbers different since I changed them by accident. I sent a second one with the numbers different since I changed them by accident . The correct question is the last image

Answer 1

Answer:

The volume of the trapezoidal ditch is 486000 in³. The volume of the half-cylinder ditch is 457812 in³. Therefore, the trapezoidal ditch holds a greater volume of water

Step-by-step explanation:

Given:

Two flood control ditches; one is a trapezoidal ditch and the other a half cylinder

To find:

the volume of the two ditches and compare which has a greater volume of water

To determine the shape with higher volume, we need to find the volume of each of the ditches

`Volume\text{ of the trapezoidal ditch = Area of the trapezoid }*\text{ distance between the ends}`
`\begin{gathered} Volume\text{ of a trapezoidal ditch = }(1)/(2)(base1\text{+ base2\rparen h }*\text{ distance between the ends} \\ \text{base 1 = 120 in, base 2 = 180in} \\ height\text{ = 90 in} \\ distance\text{ between the ends = 3ft = 36 in} \\ \\ Volume\text{ of the trapezoidal ditch = }(1)/(2)(120\text{ + 180\rparen}*90\text{ }*\text{ 36} \\ Volume\text{ of the trapezoidal ditch = 0.5 }*\text{ 300 }*\text{ 90 }*36 \\ \\ Volume\text{ of the trapezoidal ditch = 486000 in}^3 \end{gathered}`

`Volume\text{ of half cylinder = }(1)/(2)\pi r^2h`

The volume of the trapezoidal ditch is greater than the volume of the half-cylinder

The volume of the trapezoidal ditch is 486000 in³. The volume of the half-cylinder ditch is 457812 in³. Therefore, the trapezoidal ditch holds a greater volume of water