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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).

User Mike Koch
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1 Answer

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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.

Step-by-step 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.

User GaryJ
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