ShmoopTube

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Okay and here's your shmoop du jour. It's all about graphs.

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If the function for the area of a circle with respect to its diameter was graphed in the

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first quadrant... ...the graph would look like which of the following?

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Here are the potential answers...

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And hit pause, try it yourself, go on.

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First of all, we know that the equation for the area of a circle is pi times radius squared.

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Except the question is asking for the area of a circle with respect to its diameter,

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not radius.

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We know that the diameter of a circle is twice the radius, or d = 2r, and so the radius

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equals the diameter over 2.   Substituting d over 2 into the equation, we

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see that the area equals pi times d over 2 squared...

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...which equals pi over 4 times d squared. Finally, our area equation is in terms of d.

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We can convert pi over 4 into decimal format... which is roughly .8d-squared.

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Notice that this equation is a parabola and because the leading coefficient... the .8...

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is positive, it opens upwards. Looks like (C) and (D) won't work.

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The only difference between A and B is where they intersect the y-axis.

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Logically, if the diameter of a circle is 0, its area must also be 0 since... there

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wouldn't have been a circle in this case.

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This implies that the graph must go through the origin.

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Why you ask? Because the origin is the point (0,0), and on our graph, which has axies d and a.

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If d is 0, a is 0, and therefore must hit the point (0, 0). That's how the origin works. Only the graph of A does.

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Looks like our answer is A!

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We should vamoose before things get ugly...

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