The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 40 cm and 9 cm is:

41 cm

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82 cm

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62 cm

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49 cm

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Solution

The correct option is B
82 cm

Radius (r1) of 1st circle = 40 cm

Radius (r2) or 2nd circle = 9 cm

Let radius of 3rd circle be r

Area of 1st circle

Area of 2nd circle

Given that

Area of 3rd circle = area of 1st circle + area of 2nd circle

But radius cannot be negative, so radius of the third circle is 41 cm. Hence, its diameter is 82 cm.

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