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The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?
- a)14
- b)10
- c)7
- d)5
- e)4
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
The City Council has approved the construction of a circular pool in f...
The correct answer is E. First, draw the picture of the circular pool according to the information given in the problem, where the distance from the edge of the pool to the edge of the long side of the rectangular region is 2 feet. The distance from the edge of the pool to the edge of the sin short side of the rectangular region can be anything greater than 2, but it is not necessary to know this distance to solve the problem:
Now you can determine the diameter of the circular pool. The diameter is the maximum distance from one point on a circle to another (the dashed line).
Since the short side of the rectangular region is 12 feet, and the distance from the edge of the circular pool to each edge of the long sides of the rectangular region is set at 2 feet, the diameter of the circle must be 12 feet – 2(2 feet), or 12 feet – 4 feet, or 8 feet. The question asks for the radius of the pool, which is 1/2 of the diameter, or 4.
Now you can determine the diameter of the circular pool. The diameter is the maximum distance from one point on a circle to another (the dashed line).
Since the short side of the rectangular region is 12 feet, and the distance from the edge of the circular pool to each edge of the long sides of the rectangular region is set at 2 feet, the diameter of the circle must be 12 feet – 2(2 feet), or 12 feet – 4 feet, or 8 feet. The question asks for the radius of the pool, which is 1/2 of the diameter, or 4.
Community Answer
The City Council has approved the construction of a circular pool in f...
Understanding the Problem:
Given a rectangular walled area of 12 feet by 18 feet, the goal is to construct a circular pool within this area so that the pool is as large as possible while maintaining a 2-foot distance from the wall all around.
Solution:
To maximize the area of the circular pool, we need to find the largest possible radius that fits within the rectangular area.
- Step 1: Determine the dimensions of the circular pool:
- Since the pool must be 2 feet away from the wall on all sides, the usable area within the rectangular region is 12-2=10 feet by 18-2=16 feet.
- The radius of the circular pool will be half the smaller dimension of the usable area: radius = 10/2 = 5 feet.
- Step 2: Calculate the area of the circular pool:
- Area of a circle = πr^2
- Substituting the radius (5 feet) into the formula: Area = π(5)^2 = 25π square feet.
Therefore, the radius of the pool should be 5 feet to maximize the area of the circular pool within the walled area. Hence, the correct answer is option 'E' (5).
Given a rectangular walled area of 12 feet by 18 feet, the goal is to construct a circular pool within this area so that the pool is as large as possible while maintaining a 2-foot distance from the wall all around.
Solution:
To maximize the area of the circular pool, we need to find the largest possible radius that fits within the rectangular area.
- Step 1: Determine the dimensions of the circular pool:
- Since the pool must be 2 feet away from the wall on all sides, the usable area within the rectangular region is 12-2=10 feet by 18-2=16 feet.
- The radius of the circular pool will be half the smaller dimension of the usable area: radius = 10/2 = 5 feet.
- Step 2: Calculate the area of the circular pool:
- Area of a circle = πr^2
- Substituting the radius (5 feet) into the formula: Area = π(5)^2 = 25π square feet.
Therefore, the radius of the pool should be 5 feet to maximize the area of the circular pool within the walled area. Hence, the correct answer is option 'E' (5).
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The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?a)14b)10c)7d)5e)4Correct answer is option 'E'. Can you explain this answer?
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The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?a)14b)10c)7d)5e)4Correct answer is option 'E'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?a)14b)10c)7d)5e)4Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?a)14b)10c)7d)5e)4Correct answer is option 'E'. Can you explain this answer?.
The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?a)14b)10c)7d)5e)4Correct answer is option 'E'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?a)14b)10c)7d)5e)4Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?a)14b)10c)7d)5e)4Correct answer is option 'E'. Can you explain this answer?.
Solutions for The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?a)14b)10c)7d)5e)4Correct answer is option 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for ACT.
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The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?a)14b)10c)7d)5e)4Correct answer is option 'E'. Can you explain this answer?, a detailed solution for The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?a)14b)10c)7d)5e)4Correct answer is option 'E'. Can you explain this answer? has been provided alongside types of The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?a)14b)10c)7d)5e)4Correct answer is option 'E'. Can you explain this answer? theory, EduRev gives you an
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