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The figure is make up of 3 circles. The small circle has centre O and a radius of 6 cm. The big circle, has centre O and a radius of 10 cm. The diameter of the big circle cuts through the centre of the medium-sized circle and the small circle. The three regions formed are indicated as X, Y and Z
(a) Find the radius of the medium-sized circle.

(b) Find the area of region Z. Use a calculator to obtain the value of π. (Round off to nearest 2 decimal places).

(c) Express the area of the region Y as a ratio to the area of region X

 Apr 23, 2022
 #1
avatar+122388 
+1

I'm assuming here that the small circle touches the medium circle like so

 

 

 

 

(a)   The radius of the medium circle =  (6 + 10)  / 2 =   8

(b)  The area of the medium circle  =  pi * 8^2    = 64 pi

The area of Z =   area of large circle - area of medium circle =  (10^2 - 8^2) pi = 36pi ≈ 113.1 cm^2

(c)    The   area of the  small circle  = Y =  pi * 6^2  = 36pi

X is   the  area between the medium circle and  the  small circle =   (8.^2 - 6^2)  pi

 

So    Y  / X  =     36    / [ (8^2 - 6^2)  ]   =     36/28  =  9 / 7

 

 

cool cool cool 

 Apr 23, 2022
 #2
avatar+138 
+1

(a) D = 6 * 2 + (10 - 6)

         = 12 + 4 

         = 16

      r = 1/2D = 16 * 1/2 = 8

(b) Sz = π ((102) - π - (82))

          = π(100 - 64) = 113.097 cm2 ≈ 113.10 cm2

(c) Sy = π * 62 = 36π

     Sx  = π * 82 - π * 62 = 64π - 36π = 28π

       Y/X = SY/SX = 36π/28π = 9/7

 Apr 24, 2022

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