The difference between circumference and the diameter of a circle is 21.4 cm. What is the area of the circle?

Correct option is B

Given:

The difference between the circumference and the diameter of a circle is 21.4 cm.

Formula Used:

The circumference of a circle is given by C = $$2\pi r$$​, where r is the radius.

The diameter of the circle is D = 2r.

Area of the circle A = $$\pi r^2$$

Solution:

The difference between the circumference and the diameter is given as C - D = 21.4.

2πr − 2r = 21.4

2r(π−1) = 21.4

r =$$\frac{21.4}{2(\pi - 1)}$$​

r =$$\frac{21.4}{2(3.14 - 1)} = \frac{21.4}{2 \times 2.14} = \frac{10}{2} = 5 \text{ cm}$$

Area of the circle:

​$$A = \pi \times 5^2 = 25 \pi \text{ cm}^2$$​