Question

The length of a semicircle of a circle is $22cm$. The radius of the circle is:

• A. $4$ cm
• B. $5$ cm
• C. $7$ cm
• D. $11$ cm

Answer 1

The correct option is C $7$ cm

Given, length of the semicircle $=22cm$.

We know, the circumference of a semicircle $=\pi r+2r$.

Since, length of semicircle $=$ circumference of semicircle,

then, $\pi r+2r=22cm$

$⟹$ $\frac{22}{7}\times r+2r=22cm$

$⟹$ $\frac{22r+14r}{7}=22cm$

$⟹$ $\frac{36r}{7}=22cm$

$⟹$ $r=\frac{22\times 7}{36}$

$⟹$ $r=\frac{154}{36}$

$⟹$ $r=4.278cm\approx 4.3cm\approx 4cm$.

Hence, option $A$ is correct.