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The radius of one circular field is 20 m and that of another is 48 m. Find the radius of the third circular field whose area is equal to the sum of the areas of two fields.

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35 m

43 m

52 m

40 m

answer is C.

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Detailed Solution

Given the radius of one circular field is 20 m and that of another is 48 m.
According to the question,
Area of circle is

π r 2

.
The radius of 1st field is 20m.

\Rightarrow

It’s area will be

π {\times 20}^{2} .

The radius of 2nd field is 48m.

\Rightarrow

It’s area will be

π \times 48^{2} .

Area of third field = area of first field + area of second field

⇒ π r 2 = π 202 + π 482 ⇒ π r 2 = π 202 + 482

⇒ r 2 = 202 + 482

Taking square root both sides,

⇒ r = 202 + 482

⇒ r = 400 + 2304

⇒ r = 2704

⇒ r = 52 m

Therefore, the radius is 52 m.
Hence, option 3 is correct.

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