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Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimension 14cm×7cm.find the area of the remaining cardboard.?
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Two circular pieces of equal radii and maximum area, touching each oth...
Steps to Find the Area of Remaining Cardboard:
1. Find the area of the circular cutouts:
- Let the radius of each circular cutout be 'r'.
- The area of one circular cutout = πr^2
- Since there are two cutouts, the total area of the circular cutouts = 2πr^2
2. Find the area of the rectangular cardboard:
- Given dimensions of the rectangular cardboard are 14cm x 7cm.
- Area of the rectangular cardboard = Length x Breadth = 14cm x 7cm
3. Find the area of the remaining cardboard:
- Area of the remaining cardboard = Area of the rectangular cardboard - Total area of the circular cutouts
- Area of the remaining cardboard = 98cm^2 - 2πr^2
4. Maximize the area of the circular cutouts:
- Since the radius 'r' needs to be maximum, we need to make use of the entire length of the rectangle for the diameter of the circles.
- The diameter of the circle = 14cm (which is equal to the length of the rectangle)
- So, the radius of each circle (r) = 14cm / 2 = 7cm
5. Calculate the final area of the remaining cardboard:
- Substituting the value of radius 'r' = 7cm in the formula,
Area of the remaining cardboard = 98cm^2 - 2π(7)^2
Area of the remaining cardboard = 98cm^2 - 2 x 22/7 x 49
Area of the remaining cardboard = 98cm^2 - 308cm^2
Area of the remaining cardboard = 70cm^2
Therefore, the area of the remaining cardboard after cutting out two circular pieces of maximum size is 70cm^2.
1. Find the area of the circular cutouts:
- Let the radius of each circular cutout be 'r'.
- The area of one circular cutout = πr^2
- Since there are two cutouts, the total area of the circular cutouts = 2πr^2
2. Find the area of the rectangular cardboard:
- Given dimensions of the rectangular cardboard are 14cm x 7cm.
- Area of the rectangular cardboard = Length x Breadth = 14cm x 7cm
3. Find the area of the remaining cardboard:
- Area of the remaining cardboard = Area of the rectangular cardboard - Total area of the circular cutouts
- Area of the remaining cardboard = 98cm^2 - 2πr^2
4. Maximize the area of the circular cutouts:
- Since the radius 'r' needs to be maximum, we need to make use of the entire length of the rectangle for the diameter of the circles.
- The diameter of the circle = 14cm (which is equal to the length of the rectangle)
- So, the radius of each circle (r) = 14cm / 2 = 7cm
5. Calculate the final area of the remaining cardboard:
- Substituting the value of radius 'r' = 7cm in the formula,
Area of the remaining cardboard = 98cm^2 - 2π(7)^2
Area of the remaining cardboard = 98cm^2 - 2 x 22/7 x 49
Area of the remaining cardboard = 98cm^2 - 308cm^2
Area of the remaining cardboard = 70cm^2
Therefore, the area of the remaining cardboard after cutting out two circular pieces of maximum size is 70cm^2.
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Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimension 14cm×7cm.find the area of the remaining cardboard.?
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Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimension 14cm×7cm.find the area of the remaining cardboard.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimension 14cm×7cm.find the area of the remaining cardboard.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimension 14cm×7cm.find the area of the remaining cardboard.?.
Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimension 14cm×7cm.find the area of the remaining cardboard.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimension 14cm×7cm.find the area of the remaining cardboard.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimension 14cm×7cm.find the area of the remaining cardboard.?.
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