Question

True or False: The area of a circle with diameter d = 2r = 10 is greater than the area of an ellipse with major axis 2a = 10. Explain your answer. Note: the area of an ellipse is calculated with the formula = (with ‘a’ the length of the semi-major axis and ‘b’ the length of the semiminor axis).

Answer 1

Given

The area of a circle with diameter d = 2r = 10 is greater than the area of an ellipse with major axis 2a = 10.

Find

Statement is true or false.

Explanation

The area of circle is

$\pi r^2$

with radius r = 5

and area of ellipse

$\pi ab$

where a = major axis = 5

b = minor axis

as b is a minor axis it must be smaller than major axis.

so , area of ellipse is smaller than area of circle .

Final Answer

Therefore , the given statement is true.