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A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With = 22/7, the volume, in cubic ft, of the remaining part of the cone is
Correct answer is '198'. Can you explain this answer?
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Verified Answer
A right circular cone, of height 12 ft, stands on its base which has d...
We are given that diameter of base = 8 ft. Therefore, the radius of circular base = 8/2 = 4 ft
In triangle OAB and OCD
Therefore, the volume of remaining part = Volume of entire cone - Volume of smaller cone
In triangle OAB and OCD
Therefore, the volume of remaining part = Volume of entire cone - Volume of smaller cone
Most Upvoted Answer
A right circular cone, of height 12 ft, stands on its base which has d...
Given data:
- Height of the cone = 12 ft
- Diameter of the base = 8 ft
- Distance of the plane from the base = 9 ft
- Value of π (pi) = 22/7
Calculating the radius and slant height of the cone:
- Radius of the base = Diameter / 2 = 8 / 2 = 4 ft
- Slant height of the cone = √(height^2 + radius^2) = √(12^2 + 4^2) = √(144 + 16) = √160 = 4√10 ft
Calculating the volume of the original cone:
- Volume of a cone = (1/3) * π * radius^2 * height = (1/3) * (22/7) * 4^2 * 12 = (1/3) * (22/7) * 16 * 12 = (22/7) * 16 * 4 = 704 ft^3
Calculating the radius and slant height of the remaining cone:
- Distance from the base to the cut plane = 9 ft
- Radius of the remaining cone = (distance from the base to the cut plane) * (radius of the base) / (height of the cone) = 9 * 4 / 12 = 3 ft
- Slant height of the remaining cone = √(height^2 + radius^2) = √(12^2 + 3^2) = √(144 + 9) = √153 = 3√17 ft
Calculating the volume of the remaining cone:
- Volume of a cone = (1/3) * π * radius^2 * height = (1/3) * (22/7) * 3^2 * 12 = (1/3) * (22/7) * 9 * 12 = (22/7) * 9 * 4 = 99 ft^3
Determining the volume of the remaining part:
- Volume of the remaining part = Volume of the original cone - Volume of the remaining cone = 704 - 99 = 605 ft^3
Answer:
The volume of the remaining part of the cone is 605 ft^3.
- Height of the cone = 12 ft
- Diameter of the base = 8 ft
- Distance of the plane from the base = 9 ft
- Value of π (pi) = 22/7
Calculating the radius and slant height of the cone:
- Radius of the base = Diameter / 2 = 8 / 2 = 4 ft
- Slant height of the cone = √(height^2 + radius^2) = √(12^2 + 4^2) = √(144 + 16) = √160 = 4√10 ft
Calculating the volume of the original cone:
- Volume of a cone = (1/3) * π * radius^2 * height = (1/3) * (22/7) * 4^2 * 12 = (1/3) * (22/7) * 16 * 12 = (22/7) * 16 * 4 = 704 ft^3
Calculating the radius and slant height of the remaining cone:
- Distance from the base to the cut plane = 9 ft
- Radius of the remaining cone = (distance from the base to the cut plane) * (radius of the base) / (height of the cone) = 9 * 4 / 12 = 3 ft
- Slant height of the remaining cone = √(height^2 + radius^2) = √(12^2 + 3^2) = √(144 + 9) = √153 = 3√17 ft
Calculating the volume of the remaining cone:
- Volume of a cone = (1/3) * π * radius^2 * height = (1/3) * (22/7) * 3^2 * 12 = (1/3) * (22/7) * 9 * 12 = (22/7) * 9 * 4 = 99 ft^3
Determining the volume of the remaining part:
- Volume of the remaining part = Volume of the original cone - Volume of the remaining cone = 704 - 99 = 605 ft^3
Answer:
The volume of the remaining part of the cone is 605 ft^3.
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A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With = 22/7, the volume, in cubic ft, of the remaining part of the cone isCorrect answer is '198'. Can you explain this answer?
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A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With = 22/7, the volume, in cubic ft, of the remaining part of the cone isCorrect answer is '198'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With = 22/7, the volume, in cubic ft, of the remaining part of the cone isCorrect answer is '198'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With = 22/7, the volume, in cubic ft, of the remaining part of the cone isCorrect answer is '198'. Can you explain this answer?.
A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With = 22/7, the volume, in cubic ft, of the remaining part of the cone isCorrect answer is '198'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With = 22/7, the volume, in cubic ft, of the remaining part of the cone isCorrect answer is '198'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With = 22/7, the volume, in cubic ft, of the remaining part of the cone isCorrect answer is '198'. Can you explain this answer?.
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A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With = 22/7, the volume, in cubic ft, of the remaining part of the cone isCorrect answer is '198'. Can you explain this answer?, a detailed solution for A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With = 22/7, the volume, in cubic ft, of the remaining part of the cone isCorrect answer is '198'. Can you explain this answer? has been provided alongside types of A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With = 22/7, the volume, in cubic ft, of the remaining part of the cone isCorrect answer is '198'. Can you explain this answer? theory, EduRev gives you an
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