Question

3.2 mr. msomi wants the roof of his house to be painted. the roof needs two - coats of paint. one liter of paint covers an area of 16m². the paint is available in one - liter cans at a cost of r180 and in 5 - liter cans at r850 a can. labour cost r35/m². picture of the roof sketch of the roof dimension of the roof: length = 10.5m width = 10m perimeter of a rectangle = 2(l + w) area of a rectangle = l + w use the above information to answer the questions that follow. 3.2.1 how many litres of paint are needed to paint the roof? 3.2.2 which option is cost effective to buy the paint? show all yours calculations.

Explanation:

Step1: Calculate the area of the roof

The roof is a rectangle with length $l = 10.5$m and width $w = 10$m. The area of a rectangle is $A=l\times w$. So, $A = 10.5\times10=105$m². Since it needs two - coats of paint, the total area to be painted is $A_{total}=2\times105 = 210$m².

Step2: Calculate the amount of paint needed

One liter of paint covers an area of 16m². Let the amount of paint needed be $V$. Then $V=\frac{A_{total}}{16}=\frac{210}{16}=13.125$ liters.

Step3: Analyze the cost - effectiveness of paint purchase options

Option 1: One - liter cans cost R180 each.
If we buy 1 - liter cans, we need 14 cans (since we can't buy a fraction of a can) and the cost $C_1=14\times180=\text{R}2520$.
Option 2: 5 - liter cans cost R850 each.
We need $\frac{13.125}{5}=2.625$ 5 - liter cans. So we need to buy 3 5 - liter cans. The cost $C_2 = 3\times850=\text{R}2550$.

Answer:

3.2.1: 13.125 liters
3.2.2: Buying 1 - liter cans is more cost - effective.