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Question

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is

A
31 cm
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B
25 cm
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C
62 cm
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D
50 cm
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Solution

The correct option is B 50 cm
Given:
The radii of the two circles are
r1=24cm Area A1=πr12=π242cm2=576πcm2 and
r2=7cm Area A2=πr22=π72cm2=49πcm2.

So A1+A2=(576+49)πcm2=625πcm2.
This is the area A of the resulting circle.
A=A1+A2=625πcm2.
Let the diameter of this circle be d.
Now the diameter of a circle =2Aπ.
d=2625ππ cm=50 cm.

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