Bucket

How many Kč (Czech crowns) will you pay for the painting of a room in the shape of a cuboid with floor dimensions of 5 and 4 m, given the height of the room is 3 m. You will not paint the floor, the door space (210 x 90 cm), and the space behind the mirror (equilateral triangle with a side of 4 dm). You want to do a double coat, the yield of the paint is 8 m²/l, and a 5 l bucket with paint costs 300 Kč.
1. Convert all units to metres.
2. Calculate the surface of the whole cuboid.
3. Calculate the areas of the parts that will not be painted.
4. Calculate how many m² will need to be painted (do not forget the double coat).
5. Calculate how many Kč you will need for the painting (count only with whole buckets).

Final Answer:

x =  5700 Kc

Step-by-step explanation:

$$\begin{gathered} a=5\text{m} \\ b=4\text{m} \\ c=3\text{m} \\ {S}_1=2.10\cdot 0.90=1.89{\text{m}}^2 \\ {S}_2=\sqrt{3}/4\cdot 0.40^2\doteq 0.0693{\text{m}}^2 \\ {S}_3=a\cdot b+2\cdot (a+b)\cdot c=5\cdot 4+2\cdot (5+4)\cdot 3=74{\text{m}}^2 \\ S=S_3-S_1-S_2=74-1.89-0.0693\doteq 72.0407{\text{m}}^2 \\ n=\lceil S/8\cdot 2\rceil =\lceil 72.0407/8\cdot 2\rceil =19 \\ x=n\cdot 300=19\cdot 300=5700\text{Kc} \end{gathered}$$

Try another example