Elaine D.
asked • 02/14/19samantha's rectangular gift is 10 in. by 12 in. and is framed with a ribbon. She wants to use the same length of ribbon to frame a circular clock. What is the maximum radius of the circular clock?
Looking for assistance in solving this word problem. Not sure what formulas or axioms are involved.
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1 Expert Answer
Hello Elaine,
The perimeter for a rectangle is
P = 2L + 2W
→ P = 2(10) + 2(12) = 20 + 24 = 44.
Now, the perimeter of a circle (known as the circumference) is
C = 2πr
→ 44 = 2πr
→ r = 44/(2π) = 22/π ≈ 7 inches
I hope the above helps, and thank you for posting the question.
Michael E.
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Elaine D.
I just figured it out....I was getting mixed up by the word "framed," actually, and was picturing ribbon wrapped around a 3 dimensional object, the way one might see done by a "gift wrap' person- in almost a "T". Once I figured out that "framed meant, literally, the "perimeter" of a 2-dimensional (rectangle) figure, I realized what I needed to do. I applied the perimeter to the 'circumference" of a circle. [ it's "been a minute" since I've looked at geometry...42 years, in fact. ] Therefore, rounded to the nearest whole number, the maximum radius of the circular clock would be 7. Thanks for considering this question with me!!02/14/19