Question

The radii of two circle are $4$ cm and $3$ cm respectively, The diameter of the circle having area equal to the sum of the areas of the two circles(in cm) is

• A. $5$
• B. $7$
• C. $10$
• D. $14$

Answer 1

Answer: (C)

$10$

Let $r_1=4cm\&r_2=3cm$

Now, area of new circle $=\pi r_1^2+\pi r_2^2$

$\pi r^2=\frac{22}{7}({\left(4\right)}^2+{\left(3\right)}^2)$

$\frac{22}{7}\times r^2=\frac{22}{7}\times 25$

$r^2=25$

$r=5cm$

$\therefore$ Diameter of new circle $=2r=10cm$.