The top of a swimming pool is in the shape of a rectangle measuring 44 feet by 24 feet. Two of the sides of the pool are trapezoids. The water is 9 feet deep in the deep end and 3 feet deep in the shallow end.
Find the volume of the water in the pool. (Show your work.)
I really need help, the trapezoid part is confusing me. I know how to find the volume of a rectangular pool but I'm not sure about this one.
Draw a side-view of the pool to see the trapezoid, the two vertical ends are your parallel sides.
draw a horizontal from the short vertical to meet the longer vertical. You now have a rectangle and a right-angled triangle.
The rectangle is 44 by 3 and the triangle is 44 by 6
Find the area of each, add them up and multiply by the width of 24 .
Sorry, but why would I need to draw a side-view of the pool? Wouldn't I just need the above-view?
Oh wait, I understand what you mean now. Thank you!
Okay that really didn't help me much because I don't know what the pool is supposed to look like.
The top view is a rectangle
It is the side view that illustrates the shape of the pool, it will be the trapezoid.
Do you know what a trapezoid looks like ?
Yes
Reiny, if I really cared about school policies, I would not be on this website. I'm not asking you for the straight up answer, but I need to know the steps to take so I can find the answer.
I really don't understand what part of my analysis you don't get.
Volume is (base area) x (width)
So if you consider the sideview as the base, you have
rectangle = 44(3) = 132 ft^2
triangle = (1/2)(44)(6) = 132 ft^2
total area of sideview = 264 ft^2
volume = that total x 24 ft^3
44*3=132 ft^2
(44*6)*0.5=132 ft^2
132+132=264 ft^2
264*24=6,336 ft^3
v=6,336 ft^3
This apology is going to sound really stupid coming from someone who just took an hour out of your day to answer a simple enough question (multiple times), but I couldn't visualize what you were telling me with the dimensions given. I know that isn't in any way your fault because you practically gave me the answer in three different ways, and it's not like you could post a picture on here to show me.
Thank you for your descriptions, and for your time. I'm sorry it took as long as it did, and that I got mad.
To find the volume of the water in the pool, we need to calculate the volume of each section separately and then add them together. Let's break down the problem step by step:
1. Start with the rectangular section: The rectangular section of the pool measures 44 feet by 24 feet. Since the water depth is uniform throughout this section, the volume can be calculated by multiplying the length, width, and depth.
Volume of rectangular section = length × width × depth
= 44 feet × 24 feet × 3 feet (depth in the shallow end, as given)
= 3168 cubic feet
2. Moving on to the trapezoidal sections: You mentioned that two sides of the pool are trapezoids. We can divide each trapezoidal section into a rectangle and two right-angled triangles.
3. Determine the area of each trapezoidal section: We can calculate the area of a trapezoid by finding the average of the lengths of the two parallel sides (the length of the pool and the width of the pool in this case) and multiplying it by the height. Then, multiply the area by the depth to get the volume.
4. Break down the trapezoidal sections into smaller parts:
- Trapezoid 1: The length of this trapezoid is 44 feet, and the two parallel sides are 24 feet and 12 feet (difference in width at the deep and shallow ends). The height of the trapezoid is 9 feet (depth in the deep end, as given). To find the depth of the trapezoidal section, we subtract the shallow end depth from the deep end depth: 9 feet - 3 feet = 6 feet.
- Trapezoid 2: Since it is a mirror image of Trapezoid 1, we can calculate this section in the same way. The only difference is that the shallow end depth is 3 feet, and the deep end depth is 9 feet.
5. Calculate the volume of each trapezoidal section:
Volume of trapezoidal sections = ((length1 + length2) / 2) × width × depth
= (((44 + 24) / 2) × 12 feet (width of the trapezoid) × 6 feet (depth))
= 1980 cubic feet
6. Finally, add up the volumes of the rectangular and trapezoidal sections:
Total volume = Volume of rectangular section + Volume of trapezoidal sections
= 3168 cubic feet + 1980 cubic feet
= 5148 cubic feet
Therefore, the volume of water in the pool is 5148 cubic feet.