If the difference between the circumference and the diameter of a circle is 30 cm, the circumference of the circle is :

1. 44 cm

2. 45 cm

3. 46 cm

4. 48 cm

Given,

Circumference of circle - Diameter of circle = 30

$\Rightarrow 2πr - 2r = 30 \\[1em] \Rightarrow 2r(π - 1) = 30 \\[1em] \Rightarrow 2r\Big(\dfrac{22}{7} - 1\Big) = 30 \\[1em] \Rightarrow 2r(\dfrac{22 - 7}{7}) = 30 \\[1em] \Rightarrow 2r \times \dfrac{15}{7} = 30 \\[1em] \Rightarrow r = \dfrac{30 \times 7}{2 \times 15} \text{ cm}.$

Circumference of circle = 2πr

= 2 × $\dfrac{22}{7}$ × 7

= 2 × 22

= 44 cm.

Hence, option 1 is the correct option.