What happens to the area of a circle if the diameter is quadrupled?

If the diameter of a circle is quadrupled, the circle's area goes up 16 times as area is proportional to diameter squared. Remember area = pi /4 times diameter squared

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In any ratio of shapes: whatever the ratio of the lengths, the ratio of the areas is the square of that ratio.

In this case, the ratio is 1:4, so the areas are in the ratio of 1²:4² = 1:16; ie as the length of the diameter is quadrupled (ratio 1:4), the area becomes 16 times bigger (1:16).