Question

The difference between the circumference and radius of a circle is 37 cm. The area of the circle is ______.

Options

• 111 cm²

•  184 cm²

• 154 cm²

• 259 cm²

Answer 1

The difference between the circumference and radius of a circle is 37 cm. The area of the circle is 154 cm².

Explanation:

Let the radius be r cm.

We know:

Circumference of the circle = 2πr

Thus, we have:

 2πr - r = 37

⇒ r (2π - 1) = 37

`⇒ "r" (2xx22/7-1) = 37`

`=>  "r" (37/7) = 37`

`=>  "r" = (37xx7/37)`

⇒  r = 7 cm

Radius = 7 cm
Now,
Area of the circle  = πr² 

`=(22/7xx7xx7) "cm"^2`

= 154 cm²