# math

If the area of a circle increases by a factor of 9, by what factor does its circumference increase ?

1. 👍 0
2. 👎 0
3. 👁 145
1. a = pi r^2
A = pi R^2 = 9 a = 9 pi r^2
so
R^2 = 9 r^2
R = 3 r

c = 2 pi r
C = 2 pi R = 2 pi (3r) = 3 (2 pi r)
so
C = 3 c

1. 👍 0
2. 👎 0
posted by Damon
2. Since A = pi*r^2
9A = pi*(3r)^2
That is, the radius grows by a factor of 3

So, since C = 2pi*r, it also grows by a factor of 3.

Just so you know, if
the linear value grows by n,
the area grows by n^2
the volume grows by n^3

1. 👍 0
2. 👎 0
posted by Steve
3. C= 2 pi r = 2 pi (3r) = 3 ( 2 pi r )

so C = 3 c

why C = 3 c I don't understand

1. 👍 0
2. 👎 0
posted by Thomas

## Similar Questions

1. ### College Physics

If the voltage across an ohmic resistor is quadrupled, the power expended in the resistor increases by a factor of 4. decreases by a factor of 4. increases by a factor of 16. none of the preceding

asked by Lanise on February 6, 2010
2. ### math

If the area of a circle is increased by a factor of 9, the circumference of that circle will be increased by what factor? a. 3 b. 6 c. 9 d. 18 e. 81 please answer and explain

asked by Thomas on January 12, 2014
3. ### math

the dimensions of a triangle are shown below. if the height of the triangle is increased by a factor of 4, which statement will be true about the area of the triangle? a. the area will increase by the factor of 2 b. the area will

asked by Ryland on February 21, 2018
4. ### physics

In cleaning out the artery of a patient, a doctor increases the radius of the opening by a factor of two. By what factor does the cross-sectional area of the artery change?

asked by amy on September 5, 2007
5. ### math

If the side of a square increases by a factor of 3, by what factor does the area of the square increase?

asked by Thomas on January 10, 2014
6. ### science help

Two factors which cause global climate change are listed below. Factor 1: Volcanic eruptions. Factor 2: Changes in the amount of Sun’s heat received by the Earth’s atmosphere and surface. Which of these statements is correct

asked by Oscar on March 22, 2016
7. ### ECON

PLEASE CHECK AND CORRECT MY ANSWERS!!!! MRTS = marginal rate of technical substitution RTS = returns to scale MP = marginal product Suppose the production function is Cobb-Douglas and f(x1, x2) = [x1^(1/2)][x2^(3/2)]. (Note: x1

asked by Anonymous on October 14, 2009
8. ### human risk assessment

The dose for an incremental lifetime cancer risk of 10-6 (a) Increases as the estimated cancer slope factor increases (b) Decreases as the estimated cancer slope factor increases (c) Is independent of the value of the cancer slope

asked by Thano on November 3, 2007
9. ### math HELP!!!!!!!!!!

If all the dimensions of a cube are increased by 5 units, how will the surface area change? increase by a factor of 5 increase by a factor of 10 increase by a factor of 25 increase by a factor of 50