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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:

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answer is B.

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Detailed Solution

Given,
Diameter of first circle d=10 cm. So, its radius,

r_{1} = \frac{10}{2} = 5 cm

Diameter of second circle d=24 cm. Thus, its radius

r_{2} = \frac{24}{2} = 12 cm

Therefore addition of areas of both circles,

= π r_{1}^{2} + π r_{2}^{2}

= π \times 5^{2} + π \times 12^{2}

= 25 π + 144 π

= 169 π

Now this is the area of the larger circle. Thus,

Area of larger circle = π r^{2}

(r= radius of larger circle)

169 π = π r^{2}

\Rightarrow π r^{2} = 169 π

\Rightarrow r^{2} = 169

\Rightarrow r = \sqrt{169}

\Rightarrow r = 13 cm

Thus, larger circle diameter

= 13 \times 2

= 26 cm

Option 2 is correct.

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