Workbook

Surface Area and Volume Project

SURFACE AREA

You have been given all the resources required to build the pool of your dreams. Use your imagination, it could be in ground, above ground or a combination of both! It could be made of steel, plastic or concrete.

The requirements are that it is a composite shape comprised of at least three different sections and it must fit into your backyard which measures 40 ft by 25 ft. You must also follow the Virginia Health and Safety standards listed below and should show these on your drawings.

By Virginia Health and Safety standards:12 VAC 5-460-80. There shall be a deck at least four feet wide extending around the entire perimeter of the pool.

12 VAC 5-460-90. All outdoor swimming pools shall be enclosed by a substantial barrier or fence of at least three feet in height to promote safety and cleanliness of water. A gate at least three feet in height and of material as substantial as the fence or barrier shall be provided.

Now it’s your turn. Use the attached grid paper to design your pool. Make sure to include all measurements. You will need to include a top down drawing (looking at your pool as if you were in a helicopter above), and it must include all needed measurements for building.

*You must include a scale for your drawing.

You will need to include a side view of the pool to show the depth below or above ground (or both). Remember to also include all measurements required here as well.

On the page following the grid paper, you will need to calculate the interior surface area of your pool so that the contractor will know what amount of supplies are needed. Make sure to show all your work and label all calculations clearly.

Top View of Your Pool

Side View of Your Pool

Surface Area CalculationsRemember to show all your work, and don’t forget the units! Label your calculations.If you are using a vinyl liner, one estimate is that it will cost $58 per square foot. Find the cost of lining your pool. (If you are choosing another way to line your pool, include the cost per square foot and determine the cost for that.)

Fence CalculationsHow much length of fence will you need to put in? If the cost to put in a wooden fence is approximately $24/foot including labor, how much would you have to spend on the fence around your pool.

VOLUME

We will return to your pool in a little while.

But first, we are going to ask, what is the volume of your body? Is this something that is easily calculated?

No, not really. But we are going to do it!

You will need a few materials for this portion of the project:

1. Access to a measuring tape. Not a construction measuring tape, but a cloth one used in sewing. Ifyou don’t have access to this you can use a piece of string and a ruler.

2. *A bath tub - needed for a bonus part of the project.

First things first. Let’s draw a rough sketch of your body (this is not art class - but you should have basic shapes down). Provided for you is a page with room for you to sketch yourself.

Once you’ve completed your sketch there are a few questions for you to respond to. Please take the time to answer honestly and think about your methods.

Sketch Yourself #1

1. If you had to pick 1 shape to represent your body, what would it be?

2. Using your measuring tape, take the necessary measurements of that shape in relation to yourbody and calculate the volume:

3. Is this an accurate representation of the volume of your body? Why or why not? Explain.

Required Measurements: Calculation of Volume:

Let’s do it again!

This time we want you to sketch yourself again but we are going to change the method to which we cal-culate the volume of your body. Now, we want you to break your body up into three to five different 3d geometric shapes (ones that you know how to calculate the volume of, rectangular prisms, cylinders etc).

Once you have completed your drawing, calculate the volume of the shapes you suggested by taking the required measurements and using your math skills to determine the total volume of your body.

Then answers the reflection questions that follow.

Sketch Yourself (as 3 geometric shapes) #2

1. On the above diagram, draw in the different shapes you would choose to represent your body.Mark them in a different color so we can see them clearly.

2. Using your measuring tape, take the necessary measurements of that shape in relation to yourbody and the regions you’ve determined above and calculate the volume:

Required Measurements:

Calculate the total volume of your body:

Calculation of Volume:

3. Is this an accurate representation of the volume of your body? Why or why not? Explain.

4. Do you think this is a better or worse representation than the first time you sketched and estimatedyour volume? Why?

Third time’s a charm, right?

This time we want you to sketch yourself one more time, but we are going to change the amount of regions from three to at least ten different geometric shapes. That is, we want you to divide yourself into at least 10 different 3D geometric shapes and calculate the volume of those regions. Make sure you use shapes that you know how to calculate the volume of.

Once you have completed your drawing, calculate the volume of the shapes you suggested by taking the required measurements and using your math skills to determine the total volume of your body.

Then answer the reflection questions that follow.

Sketch Yourself (as geometric figures) #3

1. On the above diagram, draw in the ten different shapes you would choose to represent your body.Mark them in a different color so we can see them clearly.

2. Using your measuring tape, take the necessary measurements of that shape in relation to yourbody and the regions you’ve determined above and calculate the volume:

Required Measurements:

Calculate the total volume of your body:

Calculation of Volume:

3. Is this an accurate representation of the volume of your body? Why or why not? Explain.

4. Is this a better or worse representation that the first or second time you sketched and estimatedyour volume? Why?

Okay! This part of the project needs to be completed where you have access to a bath tub.

Now for the fun! Time to get your bathing suit on.

Did you think we were joking? I’m serious, put it on!

We are going to use the bathtub in order to figure out the volume of your body, to the best of our ability. Here are the required steps:

1. On the attached pages, you will need to sketch your bathtub. Label the measurements requiredin order for you to calculate the volume.

2. Fill the bath tub about 2/3’s full.3. Measure the depth of the water.4. Calculate the current volume of the bath tub.5. Jump in!6. Submerge yourself to the best of your ability, and with the assitance of goggles or another

person have them mark the depth the water is after you are submerged.7. Jump out! And dry off!8. Measure the depth the water was when you were submerged.9. Calculate the volume of the bath tub when you were submerged.10. Take the submerged volume and subtract from it the volume of just the water. And voila! You

have the volume of your body!

BONUS: The Bathtub

Sketch Your Tub:

You decide the views required, is one enough? Do you need more than one?

Calculations for the Volume of the Bath Tub with just Water

Calculations for the Volume of the Bathtub with You Submerged

Total Volume of Your Body:

Now, if you had your pool that you previously designed, and it was filled three-quarters of the way full. How many of you could you fit into your pool before it overflows?

Think about all the nessecary calcuations you will need to perform before you start!

Explain your steps to your calculations and your final result. Feel free to use additional pages if nessecary.

Following those calculations is a chance for you to be able to reflect on the discoveries you’ve made and what you have learned. Please take the time to answer the questions thoughtfully and honestly.

Your Pool and You

Calcuations – How Many of You Can You Fit?

Suggested Improvements:

2. Obviously our measurements are not perfect. In what ways could we have improved the accuracyof your volume? List at least three improvements you could make.

3. Given the three methods we used to estimate the volume of your body, what would you suggestto someone who needed to get an accurate value of their volume (given that they weren’t able tosubmerge themselves to find it)?

4. Why might you ever need to know the volume of your body?

5. Where else could you use the submersion technique?

6. What was something you liked about this project? What was something you’d like to see changed?

Self-Evaluation Rubric:

Students Name(s):

Part A: Rate yourself on the relative contributions that were made in preparing and submitting your project. In rating yourself, use a one-to-five point scale, where

Score for A: /20

5 = superior; 4 = above average; 3 = average; 2 = below average; 1 = weak

Category Comments Rate

Thoroughness of your calculations

Creativity brought to planning your pool

Completion of all assigned tasks on time

Your effort at all the different assigned stages of the project

Part B: Answer the following with complete sentences.

1. Describe your feelings about working on this project. Did you enjoy it? (2 marks)

2. What was the hardest part about working on this project? Explain. (2 marks)

3. List some of the things you learned while working on this project. (2 marks)

4. Were you satisfied with your final project? Elaborate. (2 marks)

5. What personal strengths did this project bring out in you? Elaborate. (2 marks)

6. If you had to do the project over again, what would you do differently? Explain. (2 marks)

Score for B:

Total for A & B:

/12

/32

Full Credit PointsNotes

Scale Drawing of Pool:5 points

Includes the scale.Shapes drawn to scale.Contains three composite shapes. Considers the state regulations. Shows all calculations.Determines the cost of the pool liner.

Fence :4 points

Find the length of the fence and show all calculations.Find the cost to install the pool.

Volume of Body (#1):8 points

Sketch is attempted validly and has accurate shapes.Necessary measurements are provided to find the volume.Volume calculations are shown and correctly determined for single shape.Answers follow-up questions in complete sentences.

Volume of Body (#2):12 points

Sketch is attempted validly and has accurate shapes.Necessary measurements are provided to find the three volumes.Volume calculations are shown and correctly determined for single shape.Overall volume is determined.Follow-up question is answered with complete sentences.

Volume of Body (#3):15 points

Sketch is attempted validly and has accurateshapes.Necessary measurements are provided to findthe ten volumes.Volume calculations are shown and correctlydetermined for single shape.Overall volume is determined.Follow-up question is answered with completesentences.

Volume of Pool:15 points

Determine the volume of your pool using eachshape. Show all necessary calculationslabeling all necessary pieces. Determine thevolume of the pool 3/4 of the way full.Based on the volume of your body, how manypeople of your volume can fit in your pool untilit overflows?

Follow-up Questions:10 points total.

Questions 2-6 - each answered in a completesentence and thoughtfully considered.

Self Evaluation:Parts A and B - total of 10 points based on percentage.

BONUS::Bonus for Water displacement volume and / or creativity.Max bonus: 10 points.

Followed all directions to determine volume bywater displacement.

Bonus added for above and beyond work orcreative landscaping around the pool oradditional cost calculations.

Surface Area and Volume ProjectName:

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