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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 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+πr22R2=(5cm)2+(12cm)2R2=25cm2+144cm2R2=169cm2R=169cmR=13cm
Thus, the diameter of the larger circle is (2×13) cm =26 cm

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