Question

Find the diameter of a circle whose circumference is $10\pi$ cm.

• A. $10$ cm
• B. $5$ cm
• C. $20$ cm
• D. $\pi$ cm

Answer 1

The correct option is A $10$ cm

Given, the circumference of the circle is $10\pi$ cm.

The circumference of the circle is given by $C=2\pi r,$ where $r$ is the radius of the circle.
$\therefore 10\pi =2\pi \times r$
Divide both sides by $2\pi$
$\Rightarrow \frac{10\pi }{2\pi }=\frac{2\pi \times r}{2\pi }$
$\Rightarrow \frac{5\times 2\pi }{2\pi }=r$
$\Rightarrow 5=r$
$\Rightarrow r=5$ cm

We know that, the diameter of the circle$\left(d\right)$ is twice its radius$\left(r\right).$
$d=2\times r$
$=2\times 5$ cm
$=10$ cm
Hence, option (a.) is the correct choice.