The length and breadth of a rectangular floor were measured and found to be 4.1 m and 2.2 m respectively. If possible error of 0.01 m was made in each of the measurements, find the:
(a) Maximum and minimum possible area of the floor
(b) Maximum possible wastage in carpet ordered to covert the whole floor
a. A = 4.1m * 2.2m = 9.02 m^2.
A max = (4.1+0.01) * (2.2+0.01) =
A min. = (4.1-0.01) * (2.2-0.01) = 8.957
m^2.
Yes
To find the maximum and minimum possible area of the floor, we need to consider the maximum and minimum values that the length and breadth can have.
Given:
Length = 4.1 m
Breadth = 2.2 m
Possible error in length = 0.01 m
Possible error in breadth = 0.01 m
(a) Maximum possible length: 4.1 + 0.01 = 4.11 m
Minimum possible length: 4.1 - 0.01 = 4.09 m
Maximum possible breadth: 2.2 + 0.01 = 2.21 m
Minimum possible breadth: 2.2 - 0.01 = 2.19 m
Maximum possible area = Maximum possible length * Maximum possible breadth
= 4.11 m * 2.21 m
≈ 9.0681 m²
Minimum possible area = Minimum possible length * Minimum possible breadth
= 4.09 m * 2.19 m
≈ 8.9671 m²
Therefore, the maximum possible area of the floor is approximately 9.0681 m², and the minimum possible area is approximately 8.9671 m².
(b) To find the maximum possible wastage in carpet, we need to calculate the difference between the maximum possible area of the floor and the nominal area of the floor.
Nominal area of the floor = Length * Breadth
= 4.1 m * 2.2 m
= 9.02 m² (rounded to two decimal places)
Maximum possible wastage = Maximum possible area - Nominal area
= 9.0681 m² - 9.02 m²
≈ 0.0481 m²
Therefore, the maximum possible wastage in carpet ordered to cover the whole floor is approximately 0.0481 m².
To find the maximum and minimum possible area of the floor, we need to consider the possible errors in the measurements.
Let's start with the maximum possible area:
1. Add the maximum error to the length: 4.1 m + 0.01 m = 4.11 m
2. Add the maximum error to the breadth: 2.2 m + 0.01 m = 2.21 m
3. Calculate the maximum possible area: Area = Length × Breadth = 4.11 m × 2.21 m = 9.0671 m² (rounded to four decimal places)
Now, let's find the minimum possible area:
1. Subtract the maximum error from the length: 4.1 m - 0.01 m = 4.09 m
2. Subtract the maximum error from the breadth: 2.2 m - 0.01 m = 2.19 m
3. Calculate the minimum possible area: Area = Length × Breadth = 4.09 m × 2.19 m = 8.9571 m² (rounded to four decimal places)
Therefore, the maximum possible area of the floor is 9.0671 m², and the minimum possible area is 8.9571 m².
Now, let's move on to finding the maximum possible wastage in carpet ordered to cover the whole floor:
1. Calculate the maximum area of the floor using the maximum measurements as discussed earlier: 9.0671 m²
2. Calculate the wastage by subtracting the maximum area from the actual area when there is no error in the measurements:
Wastage = Actual area - Maximum area
= 4.1 m × 2.2 m - 9.0671 m²
= 8.82 m² - 9.0671 m²
= -0.2471 m² (rounded to four decimal places, negative because it represents the amount needed, not wasted)
Since the wastage cannot be negative, the maximum possible wastage in carpet is 0 m².
In summary:
(a) Maximum possible area of the floor: 9.0671 m²
Minimum possible area of the floor: 8.9571 m²
(b) Maximum possible wastage in carpet ordered: 0 m²