what is the area of a section bounded by a closed elliptical whose major and minor segments measures 60cm and 45cm respectively?
To find the area of a section bounded by a closed elliptical shape, you can use the equation for the area of an ellipse.
The formula for the area of an ellipse is A = π * a * b, where "a" and "b" are the lengths of the major and minor axes, respectively.
In your case, the length of the major axis (2a) is given as 60 cm, so we can find "a" by dividing it by 2: a = 60 cm / 2 = 30 cm.
Similarly, the length of the minor axis (2b) is given as 45 cm, so we can find "b" in the same way: b = 45 cm / 2 = 22.5 cm.
Now that we have the values for "a" and "b", we can substitute them into the formula for the area of the ellipse: A = π * 30 cm * 22.5 cm.
Calculating this expression gives us the area of the section bounded by the ellipse.
To find the area of a section bounded by a closed elliptical shape, you can use the formula for the area of an ellipse.
The formula for the area of an ellipse is given by:
A = π * a * b
Where:
A is the area of the ellipse,
π is a mathematical constant approximately equal to 3.14159,
a is the length of the major axis (half of the length of the longest segment),
and b is the length of the minor axis (half of the length of the shortest segment).
In your case, the major segment measures 60 cm and the minor segment measures 45 cm. So, the lengths of the major and minor axes would be half of those measurements.
a = 60 cm / 2 = 30 cm
b = 45 cm / 2 = 22.5 cm
Now, we can plug these values into the formula to find the area:
A = π * 30 cm * 22.5 cm
Calculating the equation gives:
A ≈ 3.14159 * 30 cm * 22.5 cm
A ≈ 21159.155 cm²
Therefore, the approximate area of the section bounded by the closed elliptical shape is about 21159.155 square centimeters.