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Radius of circle .....pls show working

by Jeanel
(NY)











































A circle has an area of p square feet and a circumference of q feet. If p = 2.5q, what is the radius of the circle?


Choose Correct answer below:
A. 1.25ft
B. √2.5ft
C. 2.5ft
D. 5ft
E. 10ft

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Oct 10, 2010
Radius of Circle
by: Staff


The question:

by Jeanel
(NY)

A circle has an area of p square feet and a circumference of q feet. If p = 2.5q, what is the radius of the circle?


Choose Correct answer below:
A. 1.25ft
B. √2.5ft
C. 2.5ft
D. 5ft
E. 10ft



The answer:

Step 1: Write down what you know:

(for your information, you can create the symbol for pi on your computer by holding down the ALT key while you type 227)

R = radius of a circle

Area of a circle = πr^2

Circumference of a circle = 2πr

Area of your circle = P sq feet

Circumference of your circle = Q feet

The relationship between P and Q

P = 2.5Q

Step 2: Substitute the P and the Q in your original equations

Area of a circle = πr^2
Since P = the area of your circle

P = πr^2


Circumference of a circle = 2πr

Since Q = the Circumference of your circle

Q = 2πr

Step 3: Summarize what equations you have so far

P = πr^2

Q = 2πr

P = 2.5Q

Step 4: Substitute 2.5Q for P in the first equation

P = πr^2

P = 2.5Q
2.5Q = πr^2

Step 5: Summarize the equations that only have the same variables (in this case, Q and r)

2.5Q = πr^2

Q = 2πr

Step 6: Divide one equation by the other. This will cancel most of the variables.

(2.5Q)/Q = (πr^2)/( 2πr)

2.5 = r/2

Step 7: Multiply each side of the final equation by 2

(2.5)*2 = (r/2)*2

5 = r

The final answer is: choice D. The radius of the circle is 5 feet.

Step 8: Check your work:


P = πr^2

Q = 2πr

P = 2.5Q

P = πr^2 = π*5^2 = 25π

Q = 2πr = 2*π*5 = 10π


P = 2.5Q = (2.5)(10π) = 25π

25π = (2.5)(10π)

25π = 25π

Since 25π = 25π, the answer r = 5 feet is correct



Thanks for writing.


Staff
www.solving-math-problems.com



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