The problem
The town council wants to build a swimming pool shaped like the drawing: a rectangular prism $7$ m long, $3$ m wide and $2$ m deep that ends, at one side, in half a cylinder. Before it opens, the whole inside (the floor and the walls) must be painted and it must be filled to the top with water.
Data
- Painting $1\ \text{m}^2$ costs €$3{,}60$.
- $1\ \text{m}^3$ of water is $1000$ L and costs €$1{,}45$.
- The pool has no lid: the top is not painted.
Questions
- Sketch the pool seen from above and its walls unfolded. Which shapes make up the floor? And the walls?
- Work out the area of the floor.
- Work out the area of the walls. Careful: the curved wall is half a cylinder, and there is no straight wall where the half-cylinder joins.
- How many square metres must be painted? How much does it cost to paint the pool?
- Work out the volume of the pool in m³ and in litres.
- How much does it cost to fill it with water?
- How much does it cost in total to paint and fill it? Write the calculation as a single combined operation.
Round your results to two decimal places. Hint: the diameter of the semicircle is the width of the pool.
The solution will be posted here once we have corrected it in class.