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
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
[tex]Volume\text{ of the trapezoidal ditch = Area of the trapezoid }\times\text{ distance between the ends}[/tex][tex]\begin{gathered} Volume\text{ of a trapezoidal ditch = }\frac{1}{2}(base1\text{+ base2\rparen h }\times\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 = }\frac{1}{2}(120\text{ + 180\rparen}\times90\text{ }\times\text{ 36} \\ Volume\text{ of the trapezoidal ditch = 0.5 }\times\text{ 300 }\times\text{ 90 }\times36 \\ \\ Volume\text{ of the trapezoidal ditch = 486000 in}^3 \end{gathered}[/tex]
[tex]Volume\text{ of half cylinder = }\frac{1}{2}\pi r^2h[/tex][tex]\begin{gathered} let\text{ }\pi\text{ = 3.14, r = 90 in, } \\ \text{h = 3ft = 36 in} \\ Volume\text{ of the half cylinder = }\frac{1}{2}\times3.14\times90^2\times36 \\ Volume\text{ of the half cylinder = 457812 in}^3 \\ \\ NB:\text{ the value of the volume for the half cylinder will vary depending on the value of \pi used} \end{gathered}[/tex]
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
