The diameter of a circle is 14 cm. If it is doubled, the perimeter of the resulting circle will become:

1. four times

2. doubled

3. halved

4. three times

Given:

Diameter of the original circle = 14 cm

Radius of the original circle = r = $\dfrac{d}{2}$ = $\dfrac{14}{2}$ = 7 cm

Perimeter of the original circle = 2πr

$= 2 \times \dfrac{22}{7} \times 7\\[1em] = \dfrac{44}{7} \times 7\\[1em] = \dfrac{44}{\cancel{7}} \times \cancel{7}\\[1em] = 44 \text{ cm}$

When diameter is doubled, new diameter = 2 x 14 cm = 28 cm

New radius, r = $\dfrac{d}{2}$ = $\dfrac{28}{2}$ = 14 cm

New perimeter of circle:

$= 2 \times \dfrac{22}{7} \times 14\\[1em] = \dfrac{44}{7} \times 14\\[1em] = \dfrac{616}{7}\\[1em] = 88 \text{ cm}\\[1em]$

Thus, the new perimeter is doubled compared to the original perimeter.

Hence, option 2 is the correct option.