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:

विकल्प

• A. 34

• B. 26

• C. 17

• D. 14

Answer 1

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.