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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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A right circular cone, of height 12 ft, stands on its base which has ...
We are given that diameter of base = 8 ft. Therefore, the radius of circular base = 8/2 = 4 ft
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In triangle OAB and OCD
=>
Therefore, the volume of remaining part = Volume of entire cone - Volume of smaller cone
=> 198 cubic ft
Most Upvoted Answer
A right circular cone, of height 12 ft, stands on its base which has ...
To find the volume of the remaining part of the cone after cutting off the tip, we will use the formula for the volume of a cone and the properties of similar cones.
Initial Cone Dimensions
- Height (H): 12 ft
- Diameter: 8 ft
- Radius (R): 4 ft (since radius is half the diameter)
Volume of the Original Cone
The formula for the volume \( V \) of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
Using \( \pi = \frac{22}{7} \):
- \( V = \frac{1}{3} \times \frac{22}{7} \times (4)^2 \times 12 \)
Calculating this gives:
- \( V = \frac{1}{3} \times \frac{22}{7} \times 16 \times 12 = \frac{1}{3} \times \frac{22 \times 192}{7} = \frac{4224}{21} = 201.14 \, \text{cubic ft} \)
Dimensions of the Cut Cone
The remaining height after cutting off the top is:
- Remaining Height: \( 12 - 9 = 3 \, \text{ft} \)
Since the tip is cut off parallel to the base, the smaller cone that is removed is similar to the original cone.
Ratio of Heights
- Height Ratio: \( \frac{3}{12} = \frac{1}{4} \)
- The radius of the smaller cone: \( \frac{4}{4} = 1 \, \text{ft} \)
Volume of the Smaller Cone
Now, calculate the volume of the smaller cone:
- \( V_{\text{small}} = \frac{1}{3} \times \frac{22}{7} \times (1)^2 \times 3 \)
Calculating this gives:
- \( V_{\text{small}} = \frac{1}{3} \times \frac{22}{7} \times 3 = \frac{22}{7} = 3.14 \)
Volume of the Remaining Cone
Finally, subtract the volume of the smaller cone from the original cone:
- \( V_{\text{remaining}} = 201.14 - 3.14 = 198 \, \text{cubic ft} \)
Thus, the volume of the remaining part of the cone is 198 cubic feet.
Initial Cone Dimensions
- Height (H): 12 ft
- Diameter: 8 ft
- Radius (R): 4 ft (since radius is half the diameter)
Volume of the Original Cone
The formula for the volume \( V \) of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
Using \( \pi = \frac{22}{7} \):
- \( V = \frac{1}{3} \times \frac{22}{7} \times (4)^2 \times 12 \)
Calculating this gives:
- \( V = \frac{1}{3} \times \frac{22}{7} \times 16 \times 12 = \frac{1}{3} \times \frac{22 \times 192}{7} = \frac{4224}{21} = 201.14 \, \text{cubic ft} \)
Dimensions of the Cut Cone
The remaining height after cutting off the top is:
- Remaining Height: \( 12 - 9 = 3 \, \text{ft} \)
Since the tip is cut off parallel to the base, the smaller cone that is removed is similar to the original cone.
Ratio of Heights
- Height Ratio: \( \frac{3}{12} = \frac{1}{4} \)
- The radius of the smaller cone: \( \frac{4}{4} = 1 \, \text{ft} \)
Volume of the Smaller Cone
Now, calculate the volume of the smaller cone:
- \( V_{\text{small}} = \frac{1}{3} \times \frac{22}{7} \times (1)^2 \times 3 \)
Calculating this gives:
- \( V_{\text{small}} = \frac{1}{3} \times \frac{22}{7} \times 3 = \frac{22}{7} = 3.14 \)
Volume of the Remaining Cone
Finally, subtract the volume of the smaller cone from the original cone:
- \( V_{\text{remaining}} = 201.14 - 3.14 = 198 \, \text{cubic ft} \)
Thus, the volume of the remaining part of the cone is 198 cubic feet.
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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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