Concepts addressed: **percentages**, **rectangular prism volume**, **rectangular prism area**, **unit conversion**, **square area**.

Recommended grade: **7th**.

Difficulty level: **Basic**.

An advanced version of Building a swimming pool is also available.

**Scenario:**

This is the year –** you’re finally building an in-ground swimming pool** in your backyard! You can already see all the envious faces, but first someone’s got to do the dirty work.

- You’ve decided the pool should be
**rectangular**, with dimension**eight by thirteen feet**and**as deep as you are tall**. How much water will you need for it?

- You want to tile the inside of the pool with
**square eight by eight-inch tiles**. How many of those will you need?**Better buy 5% more**in case some of them break in the process.

**A pack of ten tiles costs $15**, and you get**$50 allowance every week**. How long will it take to save for them if**you already have $80 saved**, and you’ll be putting all your allowance towards it?

**Useful calculators:**

- Rectangular prism calculator – https://www.omnicalculator.com/math/rectangular-prism
- Volume calculator – https://www.omnicalculator.com/math/volume
- Percentage calculator – https://www.omnicalculator.com/math/percentage
- Area of a square calculator – https://www.omnicalculator.com/math/square-area
- Conversion calculator – https://www.omnicalculator.com/conversion/conversion-calculator

**Question 1 hints:**

**Question 2 hints:**

**Question 3 hints:**

**Solutions (WARNING: depend on the height, example for height being 6 feet):**

**Step-by-step solution:**

**rectangular**, so the shape of it (and therefore the shape of the water inside) will be

**a rectangular prism**. From the scenario, we know that its sides, a & b, are 8 ft and 13 ft respectively. Also, if we are 6-feet tall, the pool will

**also be this deep**, and therefore

**the height of the prism, h, is 6 ft.**

This gives us all the information we need to calculate the volume with the rectangular prism calculator:*V = a * b * h = 8 ft * 13 ft * 6 ft = 624 ft³*.

**the bottom and the four sides of the pool**, so we need to calculate

**the area of the base and the lateral faces of our rectangular prism**. All of those are rectangles, the former with sides a = 8 ft and b = 13 ft, and there are two kinds of the latter, each appearing twice (on opposite sides). The first kind is above the 8-foot side of the base, and therefore has sides a = 8 ft and h = 6 ft. The second is above the 13-foot one, having sides b = 13 ft and h = 6 ft. This allows us to calculate

**the area we want to tile**:

*A = base_area + lateral_area = a * b + 2 * a * h + 2 * b * h = 8 ft * 13 ft + 2 * 8 ft * 6 ft + 2 * 13 ft * 6 ft = 356 ft²*.

Now that we know how much area we’re working with, we need to find the number of tiles that will tile it. A single tile is **a square** of side 8 in. For our calculations, **we need the units to agree**, so let’s use the conversion calculator to write the tile side in feet: a_tile = 8 in = 2/3 ft. Therefore, the area of a square calculator states that** a single tile has an area** of:*A_tile = (a_tile)² = (2/3 ft)² = 4/9 ft²*.

Therefore, we’ll need:*A / A_tile = 356 ft ² / (4/9 ft²) = 801*

tiles to cover the whole area.

Lastly, we need to add to that number **the additional 5%** in case some of the tiles break. If we want to buy 5% more than what is required, then this means that we need 100% + 5% = 105% of what we calculated above. According to the percentage calculator, this is 105% * 801 = 841.05, which tells us that we need to buy 842 tiles.

**NOTE:** If you’ve rounded the area of a single tile to 0.44 ft² instead of keeping it as a fraction, then you could have gotten a slightly different result. You can see that in the above calculations, there is no approximation anywhere, which from the point of view of real-life scenarios, is a great thing. However, in many cases, rounding numbers is very useful. As a general tip to avoid large discrepancy we suggest doing them as late as possible.

**the cost of the tiles**. From Question 2, we know that we need 842 of them, which translates to

**85 packs**of 10 (since the tiles are not sold separately). This boils down to

*cost = 85 * pack_cost = 85 * $15 = $1,275*.

Now let’s subtract from that the amount you’ve already saved to get **how much we still need**:*money_needed = cost – money_saved = $1,275 – $80 = $1,195*.

Lastly, we must see **how many allowances** (and therefore weeks) **it will take** to save such a sum. Since we get $50 every week, we need 1,195 / 50 = 23.9, or rather 24 weeks to get that much money. But summer will be over in 24 weeks!

Oh well, maybe **next year will be the year**?

A bonus:what are you teaching next week? We'd love to prepare a scenario for you 🙂