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The area of Circle P is 4 pi. The area of Circle Q is 25 pi.

a. What is the ratio of their areas?
b. What is the ratio of their radii? Justify your reasoning.
c. The radius of Circle Q is decreased by 50%. What is the new circumference of Circle Q?

User M P
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1 Answer

20 votes
20 votes

Answer:

a. 4:25

b. 2:5

c. 15.7

Explanation:

a. By writing the ratio of circle P to circle Q, you get 4pi/25pi. Now because we have a common variable on either side, pi, we can take pi out of the ratio entirely so that the ratio between the two circles becomes 4/25, because this ratio cannot be simplified any further.
b. The equation to find the area of a circle is A = r^2 * pi. To make things easier you can just simple take pi out of the equation so that you get r^2 = 4 or 25. Knowing this, the ratio of the two radiuses are 2:5.

c. This one is easy. To start, we would make the equation: 5 (double half the the radius of circle Q) = C (circumfrence) / 3.14 (because the ratio of the circumfrence of a circle to the ratio of a circle is 3.14). By solving this equation. The circumference of circle Q is 15.7.

User Imel
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