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

Answer:

Circumference of circle B,

$C_{b}=4\ m$

Step-by-step explanation:

Given:

Let,

Circumference of circle A be Cₐ =2 2/3

∴ $C_{a} =2\frac{2}{3} \\C_{a} =\frac{8}{3}$

Radius of circle A be, rₐ

Radius of circle B be, $r_{b}=1\frac{1}{2}\times r_{a}=\frac{3}{2}\times r_{a}$

To Find:

Circumference of circle B,

$C_{b}=?$

Solution:

We have Formula for Circumference.

$Circumference=2\pi \times radius$

∴  Cₐ  = 2 × π × rₐ

∴  $\frac{8}{3}=2\pi\times r_{a}\\ \\\therefore r_{a}=\frac{4}{3\pi}$

Now

Circumference of circle B,

$C_{b}=2\pi\times r_{b}\\\\But\ r_{b}=\frac{3}{2}r_{a}\\ \\\therefore C_{b}=2\pi\times \frac{3}{2}r_{a}\\\\Put\ r_{a}=\frac{4}{3\pi} \\\\\therefore C_{b}=2\pi\times \frac{3}{2}\times \frac{4}{3\pi}\\\\\\\therefore C_{b}=4\ m$

Therefore, Circumference of circle B,

$C_{b}=4\ m$