The cost of cementing a floor 12m by 12m is N9.60. What would be the cost of cementing a floor 24m by 24m at the same rate?
Show workings
Cost of 12m by 12m = N9.60
Area of 12m by 12m = 12 x 12 = 144m2
Area of 24m by 24m = 24 x 24 = 576m2
Cost of 24m by 24m = (N9.60 x 576) / 144 = N38.40
To find the cost of cementing a floor 24m by 24m at the same rate, we can use the concept of proportions.
Let's first calculate the area of the first floor:
Area of the first floor = Length × Width
Area = 12m × 12m = 144m²
Now, let's calculate the cost per square meter for the first floor:
Cost per square meter = Total cost / Area
Cost per square meter = N9.60 / 144m²
Next, let's find the cost per square meter for the second floor:
Cost per square meter (second floor) = Cost per square meter (first floor)
Now, let's calculate the total cost for the second floor:
Total cost (second floor) = Cost per square meter (second floor) × Area (second floor)
Total cost (second floor) = Cost per square meter (first floor) × (24m × 24m)
Substituting the value of the area and cost per square meter, we have:
Total cost (second floor) = (N9.60 / 144m²) × (24m × 24m)
Now, let's calculate the cost by simplifying the equation:
Total cost (second floor) = (N9.60 / 144) × (24 × 24)
Total cost (second floor) = N9.60 × (24 × 24) / 144
Total cost (second floor) = N9.60 × 576 / 144
Total cost (second floor) = N9.60 × 4
Total cost (second floor) = N38.40
Therefore, the cost of cementing a floor 24m by 24m at the same rate would be N38.40.
Please note that the above calculations assume that the rate remains the same for both floors.
To find the cost of cementing a floor 24m by 24m at the same rate, we can use the concept of proportionality.
Let's first find the area of the floor:
Area of the floor = Length x Width
Area of the floor = 24m x 24m
Area of the floor = 576 square meters
Since the rate given is N9.60 for a floor area of 144 square meters (12m x 12m), we can set up a proportion to find the cost of cementing the larger floor:
N9.60 / 144 = x / 576
To solve for x, we can cross-multiply:
144 * x = 9.60 * 576
x = (9.60 * 576) / 144
x ≈ 38.40
So, the cost of cementing a floor 24m by 24m at the same rate would be approximately N38.40.