# Answer to Question #275 in Analytic Geometry for tommy

Question #275
In how many times will increase the square of a circle if its diameter is increased by (a) 2 times, (b) 5 times, (c) m times?
1
2010-06-09T10:51:32-0400
The radius of the circle is a half of its diameter. So if diameter is increased by m times, the radius increased by m times too. The square is expressed by the formula: S = &pi;*R&sup2;.

(a) Radius of the circle increased by 2 times. It means that m = 2. So the square of the circle increased by m&sup2; = 4 times.

(b) Radius of the circle increased by 5 times. It means that m = 5. So the square of the circle increased by m&sup2; = 25 times.

(c) Suppose that the radius was equal to R and became equal to m*R (increased by m times).
So the square of the circle was S = &pi;*R&sup2; and became S&rsquo; = &pi;(m*R)&sup2; = m&sup2;*(&pi;*R&sup2;) = m&sup2;*S. We can see that the square of the circle increased by m&sup2; times.

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