Question

circle a has a circumference 2 2/3 m. Circle B has a diameter that is 1 1/2 times long as circles a’s diameter. What is the circumference of circle b?

Answer 1

Circumference of circle B,

`C_(b)=4\ m`

Explanation:

Given:

Let,

Circumference of circle A be Cₐ =2 2/3

∴
`C_(a) =2(2)/(3) \\C_(a) =(8)/(3)`

Radius of circle A be, rₐ

Radius of circle B be,
`r_(b)=1(1)/(2)* r_(a)=(3)/(2)* r_(a)`

To Find:

Circumference of circle B,

`C_(b)=?`

Solution:

We have Formula for Circumference.

`Circumference=2\pi * radius`

∴ Cₐ = 2 × π × rₐ

∴
`(8)/(3)=2\pi* r_(a)\\ \\\therefore r_(a)=(4)/(3\pi)`

Now

Circumference of circle B,

`C_(b)=2\pi* r_(b)\\\\But\ r_(b)=(3)/(2)r_(a)\\ \\\therefore C_(b)=2\pi* (3)/(2)r_(a)\\\\Put\ r_(a)=(4)/(3\pi) \\\\\therefore C_(b)=2\pi* (3)/(2)* (4)/(3\pi)\\\\\\\therefore C_(b)=4\ m`

Therefore, Circumference of circle B,

`C_(b)=4\ m`