Area of an ellipse questions (qvault)

[Illfavor]

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I had a quick question. I feel totally lost on this problem.

"An ellipse has area equal to 24 with minor axis 8. What is half the length of the major axis?"

The area of an ellipse = pi*a*b, where a and b = the semi major/minor axes correct?
24 = pi*a*(8/2) = 4pi*a, so, a (semi-major axis)= 6/pi, which is around 1.9.

First of all, the major axis = the longest axis therefore it cannot be less than 8 as this problem demands. The answer says the major axis is 3/pi, but that is by definition the minor axis. Is this problem worded poorly or and I missing some things? Thanks!

 

[andrewhntran]

Ok, a and b are major and minor axes, not semi-major/minor axes. When substituting 8 for the minor axes and solve for a, you get 24=(pi)(a)(8) so a=3/pi. The question is asking for half the major axes, therefore, the correct answer should be (3/pi)/2 which is 3/2pi

 

[Illfavor]

I've seen on about 10 sources a and b being referred to as the semi-axes.

In the ellipse general formula, a and b are half the major and minor axes aka semi.