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what accurately describes the effect on the area of a circle if the diameter is increased by a factor of 2?

April 9, 2011 - 3:45 pm

Which statement accurately describes the effect on the area of a circle if the diameter is increased by a factor of 2?

A. The area is twice the original area
B. The area is 4 times the original area
C. The area is 8 times the original area
D. The area is 16 times the original area

Circle area = π * radius²
and since radius = diameter/2, then
Circle area = π * (diameter/2)²
Circle area = π * diameter²/4

If you increase the diameter by a factor of 2, that is the same as doubling the diameter.
Therefore, the new formula is now
Circle area = π * (2diameter)²/4
Circle area = π * 4diameter²/4

So when you compare diameter²/4 with 4diameter²/4,
you should notice that the second fraction is 4 times the first fraction.
So what does that tell you about the areas?

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One Response to “what accurately describes the effect on the area of a circle if the diameter is increased by a factor of 2?”

  1. Horatio Says:
    April 9th, 2011 at 9:34 pm

    Circle area = π * radius²
    and since radius = diameter/2, then
    Circle area = π * (diameter/2)²
    Circle area = π * diameter²/4

    If you increase the diameter by a factor of 2, that is the same as doubling the diameter.
    Therefore, the new formula is now
    Circle area = π * (2diameter)²/4
    Circle area = π * 4diameter²/4

    So when you compare diameter²/4 with 4diameter²/4,
    you should notice that the second fraction is 4 times the first fraction.
    So what does that tell you about the areas?
    References :

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