1 Answer

Aimee Jones · Answer 1 · 2021-03-28T04:42:56+0000

Given:

Circle C and circle R are similar.

The length of arc AB is
$s = (22 \pi)/(9)$

The radius of circle C (AC) = 4 unit

The radius of circle R (QR) =6 unit

To find the length of arc QP.

Formula

The relation between s, r and
$\theta$ is

$arclength = 2\pi r (\theta)/(360)$

where,

s be the length of the arc

r be the radius

$\theta$ be the angle.

Now,

For circle C

Taking r = 4

According to the problem,

$2 \pi r (\theta)/(360) = (22 \pi)/(9)$

or,
$2r (\theta)/(360) = (22)/(9)$ [ eliminating
$\theta$ from both side]

or,
$\theta = ((22)(360))/((9)(2)(4))$

or,
$\theta = 110^\circ$

Again,

For circle R

Taking, r = 6 and
$\theta = 110^\circ$ we get,

The length of arc QP is

$arc length = 2\pi (6)((110)/(360) )$

or,
$arclength = (11 \pi)/(3)$

Hence,

The length of QP is
$(11 \pi)/(3)$ . Option C.

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