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Two small circular grounds of diameters 42 m and 26 m are to be replaced by a bigger circular ground. What would be the radius of the new ground if the new ground has the same area as two small grounds?

A23 m

B25.01 m

C24.63 m

D25 m

Answer:

C. 24.63 m

Read Explanation:

Solution:

Given:

The diameter of the two small circular grounds = 42 m and 26 m respectively

Formula Used:

Area of the circle = πR2

Calculation:

The radius of the 1st circle R1 = 42/2  = 21 m

The radius of the 2nd circle R2 = 26/2 = 13 m  

Total Area of the two small ground = π(R21 + R22) = π ( 212 + 132) = π  × (441 + 169)

Total area = 610π m2

New ground area = 610π 

610π  = πR2 

⇒ R= 610

⇒ R = √610

⇒ R ≈ 24.63 m

∴ The radius of the new ground if the new ground has the same area as two small grounds is 24.63 m.


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