Question

Radius ob measures x units. which expression represents the circumference of the smaller circle with radius oa? (startfraction pi over 3 endfraction)x units (startfraction 2 pi over 3 endfraction)x units 2πx units 6πx units

Answer 1

The circumference of the smaller circle is C =  2*pi*x/3.

We have given that radius ob measures x units

What is the formula for the circumference of the circle ?

circumference of the circle is given by,

$C = 2\times \pi \times R$

where pi = 3.14

R= radius

we have two circles, A and B, where B is the larger circle and A is the smaller circle.

We know that,The circumference of B is 3 times the circumference of A.

The radius of circle B is OB = x

The radius of circle A is OA

We want to find an expression of OA.

The circumference of circle B is given by

$C(B) = 2\times \piOB = 2\times pi\times x$

The circumference of circle A  is given by

$C(A) = 2\times\pi\times OA$

we know that the circumference of circle B is 3 times the circumference of circle A,

$C(B) = 3\times C(A)$

replacing the equations for the circumferences

$2\times\pi\times x = 3\times (2\times pi\times OA)$

We have divide both sides by $2\pi$we get:

$x = 3\times OA$

Now we want to solve this for OA, then we need to isolate it,

$x/3 = OA$

We can conclude that the radius of the smaller circle is equal to x/3.

Then the circumference of circle A is

$C(A) = 2\times pi\times x/3$

To learn more about the circumference of the circle visit:

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