Question
A circular swimming pool has a radius of 20 feet. A fence is going to be built so that there is a 4-foot space around the entire pool. What is the length of the fence? Sunitha solved the problem as shown.
A circle with radius 20 feet. A larger circle is 4 feet larger than the smaller circle. Radius = 24 feet. Circumference = 24 pi.
What was her error?
She should have used 12 in the formula, not 24.
She forgot to multiply the radius by 2 in the formula.
She did not add the additional fence length to the pool’s radius.
She should have used 4 ft in the formula.
A circle with radius 20 feet. A larger circle is 4 feet larger than the smaller circle. Radius = 24 feet. Circumference = 24 pi.
What was her error?
She should have used 12 in the formula, not 24.
She forgot to multiply the radius by 2 in the formula.
She did not add the additional fence length to the pool’s radius.
She should have used 4 ft in the formula.
Answers
GPT-4o mini
Sunitha's error is: **She did not add the additional fence length to the pool’s radius.**
She correctly identified that the radius of the larger circle (which represents the space around the pool) is 24 feet (20 feet for the pool's radius plus 4 feet for the space). However, she should have calculated the circumference using this new radius. Since she mentioned "Circumference = 24 pi," it seems she is calculating the circumference correctly.
Thus, the issue is not with how she calculated the circumference, but rather with misunderstanding the correct radius to consider and context in which she stated "Circumference = 24 pi." She should clearly indicate that she was indeed using the correct radius (24 feet) while calculating the circumference.
In summary, she did add the additional space to the radius, but her in-depth explanation was unclear, which led to confusion about her understanding. However, if we are strictly interpreting the answer choices provided, the statement that fits best is regarding not adding the additional fence length correctly in the explanation.
She correctly identified that the radius of the larger circle (which represents the space around the pool) is 24 feet (20 feet for the pool's radius plus 4 feet for the space). However, she should have calculated the circumference using this new radius. Since she mentioned "Circumference = 24 pi," it seems she is calculating the circumference correctly.
Thus, the issue is not with how she calculated the circumference, but rather with misunderstanding the correct radius to consider and context in which she stated "Circumference = 24 pi." She should clearly indicate that she was indeed using the correct radius (24 feet) while calculating the circumference.
In summary, she did add the additional space to the radius, but her in-depth explanation was unclear, which led to confusion about her understanding. However, if we are strictly interpreting the answer choices provided, the statement that fits best is regarding not adding the additional fence length correctly in the explanation.