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 B
26
Let r1 and r2 be the radii of hte two given circles. Given, 2r1=10cm ∴r1=5cm Aslo, 2r2=24cm ∴r2=12cm Let R be the radius of the larger circle. Given, area of larger circle =Sum of areas of two given circles ∴πR2=πr21+πr22⇒R2=(5cm)2+(12cm)2⇒R2=25cm2+144cm2⇒R2=169cm2⇒R=√169cm⇒R=13cm Thus, the diameter of the larger circle is (2×13) cm =26 cm