Problem:
When the circumference of a toy balloon is increased from 20 inches to 25 inches, the radius is increased by:
Answer Choices:
A. 5 in.
B. 221β in.
C. 5/Ο in.
D. 5/2Ο in.
E. Ο/5 in.
Solution:
Let C1β and C2β be the final and original circumferences, and r1β and r2β be the final and original radii. The formula for circumference is C=2Οr. We need to find the change in radius, r1ββr2β, as the circumference increases from 20 to 25.
C1ββC2β25β205r1ββr2ββ=2Οr1ββ2Οr2β=2Ο(r1ββr2β)=2Ο(r1ββr2β)=2Ο5ββ
Therefore the increase in the radius is 2Ο5ββ units.