Question

State whether true or false.

The radii of two circles are $19$ cm and $9$ cm respectively. The radius of the circle which has the circumference equal to the sum of the circumferences of the two circles is $26$ cm.

• A. True
• B. False

Answer 1

The correct option is B False

Circumference of a circle, $C$ $=$ $2\pi r$
$\Rightarrow C_1$= $2\times \frac{22}{7}\times 19$

$\Rightarrow C_2$= $2\times \frac{22}{7}\times 9$

$\Rightarrow C_1+C_2=2\times \frac{22}{7}(19+9)$

$\Rightarrow 2\times \frac{22}{7}\times r=176$

$r=28$ cm