The concentric circles on a target are 5 inches apart. The inner circle (red) has a perimeter of 31.4 inches. What is the perimeter of the next largest circle?

Question

This is for pre calc. trying to find the perimeter of outer circle

 

Answer 1

Hi Kiyana, the perimeter or circumference of a circle is given by the equation: c = pi * d. We are given the perimeter of the inner circle as 31.4 inches. Use that to find d.

 

Find the diameter of the inner circle.

 

c = pi * d

 

Let pi = 3.14

 

31.4 = 3.14 * d

 

Divide both sides by 3.14 gives:

 

d = 10 inches.

 

The diameter of a circle is given by: d = 2 * r, where d is the diameter and r is the radius.

 

Then the radius of the inner circle is 5 inches, 10 / 2 = 5.

 

Find the perimeter of next largest circle.

 

Remember, c = pi * d.

 

For the next circle, the diameter will be the radius of the inner circle, 5 inches, + 5 inches times 2, or 20 inches

 

c = 3.14 * 20

 

c = 62.8 inches.

 

Solution: perimeter of next circle equals 62.8 inches.

 

Questions?

 

Answer 2

perimeter of 31.4 in  = 2πr

thus r = 31.4/(2*3.14) = 5 in.

radius of the next circle is thus 5 + 5 = 10 in 

perimeter of next circle is then 2π*10 = 62.8 in