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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?

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32 cm

54 cm

26 cm

10 cm

answer is C.

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Detailed Solution

The radius of the plate with diameter 10 cm is

r 1 = 102 = 5 c m

, and with diameter 24 cm is

r 2 = 242 = 12 c m

.
We know that the area of the circle is

A = π r 2

.
Substitute

r 1 = 102 = 5 c m

in the above formula, and we have

A 1 = π (5) 2 = 25 π c m 2

Substitute

r 2 = 242 = 12 c m

in the above formula, and we have

A 2 = π (12) 2 = 144 π c m 2

Add both the areas, and we get

A = (25 π + 144 π) c m 2 = 169 π c m 2

Now, the area of the bigger plate is

169 π c m 2

. To find the radius R, we have

π R 2 = π 169 R 2 = 169 R = 169 R = 13 c m

Therefore, the diameter of the bigger plate is

13 × 2 = 26 c m

.
Hence, the correct option is 3.

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