Question

Given a circle with measures of (C, d, and r) and a circle with measures of (C', d', and r'), what is r if C C' = 5 and d' = 20? A) 10 B) 25 C) 50 D) 100

Answer 1

C) The value of r = 50 units.

Explanation:

Measure of Circle 1 are (C, d, and r)

and Measure of Circle 2 are (C', d', and r')

Also, C /C' = 5 and d' = 20

CIRCUMFERENCE OF A CIRCLE = 2 π x RADIUS

= π x DIAMETER (as D = 2 x Radius)

Circumference of Circle 1 : C = π x d

Circumference of Circle 2 : C' = π x d'

`(C)/(C')  = (\pi * d)/(\pi * d') \\\implies5 = (d)/(20)    \implies d = 100`

⇒ d = 100

As D = 2 x Radius .⇒ r = d/2 = 100/2 = 50

or, r = 50

Hence, the value of r = 50 units.

Answer 2

The value of radius r is 50

Explanation:

Given as :

The measure of two circles as

Circumference = c Circumference = c'

Diameter = d Diameter = d'

Radius = r Radius = r'

And

`(c)/(c')` = 5

d' = 20

∴ circumference of circle =
`2* \Pi * r` =
`\Pi * d`

Or,
`(c)/(c')` =
`(2\pi r )/(\pi d')`

Or, 5 =
`(2r)/(d')`

Or, 5 =
`(2r)/(20)`

∴ 2 × r = 5 × 20

I.e r = 50

Hence The value of radius r is 50 Answer