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?

# 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  , and with diameter 24 cm is  .
We know that the area of the circle is  .
Substitute   in the above formula, and we have

Substitute   in the above formula, and we have

Add both the areas, and we get

Now, the area of the bigger plate is  . To find the radius R, we have

Therefore, the diameter of the bigger plate is  .
Hence, the correct option is 3.

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