MathematicsThe diameter of two circular plates are 10 cm and 24 cm respectively. What is the diameter of the plate which has an area equal to the combined area of the two given plates?

The diameter of two circular plates are 10 cm and 24 cm respectively. What is the diameter of the plate which has an area equal to the combined area of the two given plates?


  1. A
    32 cm
  2. B
    54 cm
  3. C
    26 cm
  4. D
    10 cm

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    Solution:

    The radius of the plate with diameter 10 cm is r 1 = 10 2 =5cm  , and with diameter 24 cm is r 2 = 24 2 =12cm  .
    We know that the area of the circle is A=π r 2  .
    Substitute r 1 = 10 2 =5cm   in the above formula, and we have
    A 1 =π (5) 2 =25πc m 2  
    Substitute r 2 = 24 2 =12cm   in the above formula, and we have
    A 2 =π (12) 2 =144πc m 2  
    Add both the areas, and we get
    A=(25π+144π)c m 2 =169πc m 2  
    Now, the area of the bigger plate is 169πc m 2  . To find the radius R, we have
    π R 2 =π169 R 2 =169 R= 169 R=13cm  
    Therefore, the diameter of the bigger plate is 13×2=26cm  .
    Hence, the correct option is 3.
     
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