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
• B. 26
• C. 17
• D. 14

Answer 1

The correct option is B

26

Let $r_1$ and $r_2$ be the radii of hte two given circles.
Given, $2r_1=10cm$
$\therefore r_1=5cm$
Aslo, $2r_2=24cm$
$\therefore r_2=12cm$
Let R be the radius of the larger circle.
Given, area of larger circle =Sum of areas of two given circles
$\therefore \pi R2=\pi r_1^2+\pi r_2^2\Rightarrow R^2=(5cm{)}^2+(12cm{)}^2\Rightarrow R^2=25c{m}^2+144c{m}^2\Rightarrow R^2=169c{m}^2\Rightarrow R=\sqrt{169}cm\Rightarrow R=13cm$
Thus, the diameter of the larger circle is $(2\times 13)$ cm =26 cm