A = πr^2
∆A ≈ dr ∆r = 2π*40*(49-40) = 720π
actual change is π(49^2 - 40^2) = 801π
not very close, since ∆r is so big.
The estimated change in area is nothing mm2.
∆A ≈ dr ∆r = 2π*40*(49-40) = 720π
actual change is π(49^2 - 40^2) = 801π
not very close, since ∆r is so big.
We know that the formula for the area of a circle is A = πr^2, where A represents the area and r is the radius.
Initially, the area (A1) with a radius of 40 mm is given by A1 = π(40)^2.
At the end, when the radius is 49 mm, the area (A2) can be calculated as A2 = π(49)^2.
Now, to find the approximate change in area, we subtract the initial area from the final area: A2 - A1.
Using this formula, the estimated change in area is nothing mm²... Oh wait, that can't be right! Let me recalculate that for you.
Calculating... recalculating... yup, I made a clownish mistake earlier. The estimated change in area is actually approximately 17,798 mm².
Keep in mind that this is an approximation since we used the radius values, not the precise measurements. But hey, that should give you a good idea of the increase in the bacterial colony's area.
Area = π * r^2
Given that the radius increases from 40 mm to 49 mm, we can calculate the change in area as follows:
Old Area = π * (40 mm)^2
New Area = π * (49 mm)^2
To find the approximate increase in area, we can subtract the old area from the new area:
Approximate Increase in Area = New Area - Old Area
≈ (π * (49 mm)^2) - (π * (40 mm)^2)
≈ π * (49^2 mm^2 - 40^2 mm^2)
Simplifying the expression within parentheses:
≈ π * (2401 mm^2 - 1600 mm^2)
≈ π * 801 mm^2
Therefore, the approximate increase in area is approximately 801 mm².
The area of a circle can be calculated using the formula: A = πr², where A represents the area and r represents the radius.
When the radius is 40 mm, the initial area will be:
A1 = π(40 mm)²
When the radius increases to 49 mm, the final area will be:
A2 = π(49 mm)²
To find the approximate increase in area, we subtract the initial area from the final area:
Approximate increase in area = A2 - A1
Let's calculate it step by step:
Initial area (A1):
A1 = π(40 mm)²
Calculating A1:
A1 = π(1600 mm²)
A1 ≈ 5026.548 mm² (using the value of π as approximately 3.14159)
Final area (A2):
A2 = π(49 mm)²
Calculating A2:
A2 = π(2401 mm²)
A2 ≈ 7539.816 mm² (using the value of π as approximately 3.14159)
Approximate increase in area:
Approximate increase in area = A2 - A1
Approximate increase in area ≈ 7539.816 mm² - 5026.548 mm²
Approximate increase in area ≈ 2513.268 mm²
Therefore, the approximate increase in area of the bacteria colony is 2513.268 mm².