The sum of diameters of two circles is 14cm and the difference of their circumference is 8cm. Find the circumferences of the two circles.

Question

Sum of mensuration class 9 on circle.

Answer 1

Let x = diameter circle 1

Let y = diameter circle 2

 

sum of diameters is 14cm

x + y = 14

 

difference of circumferences is 8cm

∏x - ∏y = 8

∏(x-y) = 8

x - y = 8/∏

 

We have two equations:

x + y = 14

x - y = 8/∏     add equations

--------------

2x = 14 + 8/∏

x = (14+8/∏)/2

x = 7 + 4/∏

 

Replace x with 7+4/∏ in one of the original equations

 

x + y = 14

7+4/∏ + y = 14

y = 14 - 7 - 4/∏

y = 7 - 4/∏

 

Diameter of circle 1:  7 + 4/∏

Circumference of circle 1

∏(7+4/∏) = 7∏ + 4

 

Diameter of circle 2: 7 - 4/∏

Circumference of circle 2:

∏(7-4/∏) = 7∏-4

 

Check answer:

x + y = 14

7+4/∏ + 7 - 4/∏ = 14

14 = 14  

Yes

 

∏(x-y) = 8

∏(7+4/∏ - (7-4/∏)) = 8

∏(7 + 4/∏ - 7 + 4/∏) = 8

∏(8/∏) = 8

8 = 8

Yes

 

 

Answer 2

Let x = diameter 1

Let y = diameter 2

 

Using these variables, we can create two equations.

 

x + y = 14                      eq1   ------>  sum of the diameter

π(x - y) = 8                 

 

x - y = 8/π                     eq2   -------> difference between the circumferences

 

 

Use the substitution/elimination method to solve for x and y.  Then once you have the numerical values of x and y, multiply them individually by π to get their circumference.

 

Subtract eq2 from eq1 to eliminate the x terms.

 

2y = 14 - (8/π)

 

  y = (1/2)[(14π - (8/π)]

 

  y = 8π - (4/π)

 

  y = (32π - 4) / π

 

 

The plug in this value of y into eq1 to solve for x.

 

x + ((32π - 4) / π) = 14

 

 

Solve for x.