The circumference of a circle is 30$$\pi$$​ cm. What is its area (in cm²)?

Correct option is B

Given:

the circumference of a circle is $30\pi$ cm

Formula Used:

The formula for the circumference $C$ of a circle is: C = 2πr

The formula for the area $A$ of a circle is: $$A=πr^2$$

where $r$ is the radius of the circle.​​

Solution:

We are told that the circumference is $30\pi$ cm, so:

​$$30π=2πr$$ 

​$$r = \frac{30\pi}{2\pi} = 15$$​​

So, the radius $r=15$ cm.

Substitute $r=15$into the area formula:​

$$A = \pi (15)^2 = \pi \times 225 = 225\pi$$ 

So, the area = $$225\pi$$.