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: - Mathematics

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MCQ

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:

Options

  • A. 34

  • B. 26

  • C. 17

  • D. 14

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Solution

Let r1 and r2 be the radii of the two given circles.

Given, 2r1 = 10 cm

∴ r1 = 5 cm

Also, 2r2 = 24 cm

∴ r2 = 12 cm

Let R be the radius of the larger circle.

Given, area of larger circle = Sum of areas of two given circles

`therefore piR^2=pir_1^2+pir_2^2`

`rArr R^2=(5cm)^2+(12cm)^2`

`rArr R^2=25^2+144cm^2`

`rArr R^2=169cm^2`

`rArr R^2=sqrt169cm`

`rArr R^2=13cm`

Thus, the diameter of the larger circle is (2 × 13) cm = 26 cm

Hence, the correct answer is B.

  Is there an error in this question or solution?
2011-2012 (March) Delhi Set 1

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