Question

If the difference between the circumference and radius of a circle is 37 cm, then its area is 

Options

• 154 cm²

• 160 cm²

•  200 cm²

• 150 cm²

Answer 1

We have given the difference between circumference and radius of the circle.

Let C be the circumference, r be the radius and A be the area of the circle.

Therefore, from the given condition we have

`C-r=2pir-r`

`∴ 37=2pir-r`

`∴37=r(2pi-1)`

`∴ r=37/((2pi-1))`

Now we will substitute `pi=22/7`

`∴ r= 37/((2xx22/7-1))`

`∴ r=37/((44/7-1))`

`∴ r=37/(((44-7)/7))`

`∴ r=37/((37/7))` 

`∴ r=37xx7/37`

`∴ r=7`

Now we will substitute the value of r in`A=pir^2`.

`∴ A=pixx7^2`

Now we will substitute` pi=22/7`

`∴ A=22/7xx7^2`

`∴=22xx7`

`∴ A=154`

Therefore, area of the circle is `154 cm^2`