Question

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters $36cm$ and $20cm$ is

• A. $56cm$
• B. $42cm$
• C. $28cm$
• D. $16cm$

Answer 1

Answer: (C)

$28cm$

Given-

The diameter of the two circles are

$d_1=36cm\Rightarrow$ radius $r_1=\frac{d_1}{2}=\frac{36}{2}cm=18cm$ and

$d_2=20cm\Rightarrow$ radius $r_2=\frac{d_2}{2}=\frac{20}{2}cm=10cm.$

$\therefore$ The circumference $C_1=2\pi r_1=2\pi \times 18cm=36\pi cm$ and

The circumference $C_2=2\pi r_2=2\pi \times 10cm=20\pi cm$

So $C_1+C_2=(36+20)\pi cm=56\pi cm.$

This is the circumference $C$ of the resulting circle.

$\therefore C=C_1+C_2=56\pi cm$

Let the radius of this circle be $r.$

Now, the radius of a circle $=\frac{\text{circumference}}{2\pi }$

$\therefore r=\frac{56\pi }{2\pi }cm=28cm.$