The sum of the lengths of a semicircular bow and its string is 360 cm. The length of the bow is :

1. 214 cm

2. 216 cm

3. 218 cm

4. 220 cm

Given,

The sum of the lengths of a semicircular bow and its string is 360 cm.

∴ Arc length + Diameter = 360

$\Rightarrow πr + 2r = 360 \\[1em] \Rightarrow \dfrac{22}{7} \times r + 2r = 360 \\[1em] \Rightarrow \dfrac{22r + 14r}{7} = 360 \\[1em] \Rightarrow \dfrac{36r}{7} = 360 \\[1em] \Rightarrow r = 70 \text{ cm}.$

Length of the bow = πr

= $\dfrac{22}{7}$ × 70

= 220 cm.

Hence, option 4 is the correct option.