Question

Radius OB measures x units. Which expression represents

the circumference of the smaller circle with radius OA?
of
olex units
(x units
021x units
0 6ux units

Answer 1

Circumference of the smaller circle = 2.1x units

Explanation:

Given question is incomplete; here is the complete question.

Two similar circles are shown. The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA ?

Radius of the larger circle OB = x units

Radius of the smaller circle OA = y units

Circumference of larger circle = 2πx units

Circumference of smaller circle = 2πy units

Since circumference of larger circle is 3 times the circumference of smaller circle,

2πx = 3(2πy)

2πx = 6πy

x = 3y

y =
`(x)/(3)`

Therefore, circumference of the smaller circle =
`2\pi ((x)/(3))` units

=
`(2\pi x)/(3)` units

= 2.094x

≈ 2.1x

Circumference of the smaller circle circle = 2.1x units