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An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use p = 22/7]
- a)402.12 cm2
- b)298 cm2
- c)377.14 cm2
- d)315 cm2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
An inverted cone of vertical height 12 cm and the radius of base 9 cm ...
Since, Δ OAB ~ Δ OCD
⇒ CD = 3 cm
Slant height of cone (/) = 
= 15 cm
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Community Answer
An inverted cone of vertical height 12 cm and the radius of base 9 cm ...
Given:
Vertical height of the inverted cone, h = 12 cm
Radius of the base, r = 9 cm
Depth of the water, d = 4 cm
To find:
The area of the interior surface of the cone not in contact with the water.
Formula Used:
The formula to find the area of the curved surface of a cone is given by:
Curved Surface Area of Cone = πrl
where r is the radius of the base and l is the slant height of the cone.
The formula to find the slant height of a cone is given by:
Slant Height of Cone = √(h^2 + r^2)
Calculation:
1. Slant Height of the Cone:
Using the formula for the slant height of a cone,
Slant Height of Cone = √(h^2 + r^2)
Slant Height of Cone = √(12^2 + 9^2)
= √(144 + 81)
= √225
= 15 cm
2. Curved Surface Area of the Cone:
Using the formula for the curved surface area of a cone,
Curved Surface Area of Cone = πrl
Curved Surface Area of Cone = (22/7) * 9 * 15
= (22/7) * 135
= 420 cm^2
3. Area of the Water Surface:
The area of the water surface can be calculated by finding the area of the circle formed at the water level.
Area of Circle = πr^2
= (22/7) * 9^2
= (22/7) * 81
= 254.57 cm^2
4. Area of the Interior Surface not in Contact with Water:
Area of the Interior Surface = Curved Surface Area of Cone - Area of Water Surface
= 420 - 254.57
= 165.43 cm^2
Therefore, the area of the interior surface of the cone not in contact with the water is 165.43 cm^2.
Hence, the correct answer is option C) 377.14 cm^2.
Vertical height of the inverted cone, h = 12 cm
Radius of the base, r = 9 cm
Depth of the water, d = 4 cm
To find:
The area of the interior surface of the cone not in contact with the water.
Formula Used:
The formula to find the area of the curved surface of a cone is given by:
Curved Surface Area of Cone = πrl
where r is the radius of the base and l is the slant height of the cone.
The formula to find the slant height of a cone is given by:
Slant Height of Cone = √(h^2 + r^2)
Calculation:
1. Slant Height of the Cone:
Using the formula for the slant height of a cone,
Slant Height of Cone = √(h^2 + r^2)
Slant Height of Cone = √(12^2 + 9^2)
= √(144 + 81)
= √225
= 15 cm
2. Curved Surface Area of the Cone:
Using the formula for the curved surface area of a cone,
Curved Surface Area of Cone = πrl
Curved Surface Area of Cone = (22/7) * 9 * 15
= (22/7) * 135
= 420 cm^2
3. Area of the Water Surface:
The area of the water surface can be calculated by finding the area of the circle formed at the water level.
Area of Circle = πr^2
= (22/7) * 9^2
= (22/7) * 81
= 254.57 cm^2
4. Area of the Interior Surface not in Contact with Water:
Area of the Interior Surface = Curved Surface Area of Cone - Area of Water Surface
= 420 - 254.57
= 165.43 cm^2
Therefore, the area of the interior surface of the cone not in contact with the water is 165.43 cm^2.
Hence, the correct answer is option C) 377.14 cm^2.
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An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use p = 22/7]a)402.12 cm2b)298 cm2c)377.14 cm2d)315 cm2Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use p = 22/7]a)402.12 cm2b)298 cm2c)377.14 cm2d)315 cm2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use p = 22/7]a)402.12 cm2b)298 cm2c)377.14 cm2d)315 cm2Correct answer is option 'C'. Can you explain this answer?.
An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use p = 22/7]a)402.12 cm2b)298 cm2c)377.14 cm2d)315 cm2Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use p = 22/7]a)402.12 cm2b)298 cm2c)377.14 cm2d)315 cm2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use p = 22/7]a)402.12 cm2b)298 cm2c)377.14 cm2d)315 cm2Correct answer is option 'C'. Can you explain this answer?.
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An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use p = 22/7]a)402.12 cm2b)298 cm2c)377.14 cm2d)315 cm2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use p = 22/7]a)402.12 cm2b)298 cm2c)377.14 cm2d)315 cm2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use p = 22/7]a)402.12 cm2b)298 cm2c)377.14 cm2d)315 cm2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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