Question

The area of an ellipse with axes of length 2a and 2b is A= (π)(a)(b).

Approximate the percent change in the area when a increases by 2 % and b increases by 1.5 %

Answer 1

To find the percent change in the area of an ellipse when the axes increase by certain percentages, we can use the formula for percent change.

Step-by-step explanation:

The area of an ellipse is given by the formula A = πab, where a is half the length of the major axis and b is half the length of the minor axis. To find the percent change in the area when a increases by 2% and b increases by 1.5%, we can use the formula:

Percent change = ((New Area - Old Area) / Old Area) * 100%

Let's calculate the new area:

New Area = π * (a + 0.02a) * (b + 0.015b)

Old Area = πab

Now we can substitute these values into the percent change formula and simplify to find the approximate percent change in the area.