Question

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii $15cm$ and $18cm.$

• A. $44cm$
• B. $22cm$
• C. $33cm$
• D. $66cm$

Answer 1

The correct option is C $33cm$

Given:

The radii of two circles are $r_1=15cm$ & $r_2=18cm.$

To find out:

The radius $r$ of the circle whose circumference $C=C_1+C_2.$

Solution:

We have $C_1=2\pi r_1$ & $C_2=2\pi r_2.$

$\therefore$ The resulting circumference $C=2\pi r=C_1+C_2=2\pi (r_1+r_2)$

$=2\pi (15+18)cm=66\pi cm.$

$\therefore$ We have, $2\pi r=66\pi \Rightarrow r=\frac{66}{2}cm=33cm.$