Question

The circumferences of two circles are in the ratio of 2:5. The radius of the smaller circle is 16 in. What is the radius of the larger circle?

32 in.

40 in.

80 in.

160 in.

Answer 1

\[\frac{5}{2}=\frac{x}{16}\iff x=\frac{5\times16}{2}\]

Answer 2

\[\frac{ C_{1} }{ C _{2} } = \frac{ 2 }{ 5 }; C _{2}= C_{1}\frac{ 5 }{ 2 }\]
\[2pir = \frac{ 2\pi(16)(5) }{ 2 }; r = \frac{ 16*5 }{ 2 } = 40\]