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Question

If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm)is:

A
34
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B
26
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C
17
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D
14
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Solution

The correct option is A 26
Radius of the first circle r1=102=5 cm.

Radius of the second circle r2=242=12 cm.

Sum of their area = πr12+πr22

=π52+π122

=25π+144π=169π.

Let the radius of the larger circle be r.

Area=πr2.

According to the question:

πr2=169π

r2=169

r=169=13 cm

Radius of the large circle=13 cm.

Then, diameter of the larger circle=13×2=26 cm.

Therefore, option B is correct.

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