A platform was originally designed as a rectangle 12.00 meters long and 8.00 meters wide. The rectangular design is replaced with a platform in the shape of an ellipse. The elliptical platform will have the same area as the original rectangular platform and the major axis is 16.00 meters. Determine the minor axis rounded to 3 significant digits.
The area of the rectangular platform is found by multiplying the length by the width:
Area = 12.00 m * 8.00 m = 96.00 m^2
The formula for the area of an ellipse is:
Area = π * a * b
where a is the semi-major axis and b is the semi-minor axis.
Since the major axis of the ellipse is given as 16.00 meters (the full major axis would be 2a), we can divide it by 2 to find the semi-major axis:
a = 16.00 m / 2 = 8.00 m
To find the semi-minor axis, we can rearrange the formula for the area of an ellipse:
b = Area / (π * a)
b = 96.00 m^2 / (π * 8.00 m)
b ≈ 3.817 m
Rounded to 3 significant digits, the minor axis of the elliptical platform is approximately 3.82 meters.