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The area of base of a conical vessel is 75.46 dm2 and its volume is 226.38 dm3. The height of the conical vessel is
- a)15 dm
- b)6 dm
- c)9 dm
- d)12 dm
Correct answer is option 'C'. Can you explain this answer?
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The area of base of a conical vessel is 75.46 dm2and its volume is 226...
To find the height of the conical vessel, we need to use the formulas for the volume and the area of the base of a cone.
Given:
Area of base = 75.46 dm^2
Volume = 226.38 dm^3
1. Finding the radius of the base:
The formula for the area of the base of a cone is A = πr^2, where A is the area and r is the radius.
75.46 = πr^2
2. Solving for the radius:
Divide both sides of the equation by π:
75.46/π = r^2
r^2 = 24
Take the square root of both sides to find the radius:
r = √24
r ≈ 4.9 dm
3. Finding the height of the cone:
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
226.38 = (1/3)π(4.9)^2h
4. Solving for the height:
Multiply both sides of the equation by 3/π:
(3/π) * 226.38 = (3/π)(1/3)π(4.9)^2h
(3/π) * 226.38 = 4.9^2h
Divide both sides of the equation by (4.9)^2:
(3/π) * 226.38 / (4.9)^2 = h
5. Calculating the height:
Using a calculator, evaluate the right side of the equation:
h ≈ 8.9 dm
Therefore, the height of the conical vessel is approximately 8.9 dm, which is closest to option 'C' (9 dm).
Given:
Area of base = 75.46 dm^2
Volume = 226.38 dm^3
1. Finding the radius of the base:
The formula for the area of the base of a cone is A = πr^2, where A is the area and r is the radius.
75.46 = πr^2
2. Solving for the radius:
Divide both sides of the equation by π:
75.46/π = r^2
r^2 = 24
Take the square root of both sides to find the radius:
r = √24
r ≈ 4.9 dm
3. Finding the height of the cone:
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
226.38 = (1/3)π(4.9)^2h
4. Solving for the height:
Multiply both sides of the equation by 3/π:
(3/π) * 226.38 = (3/π)(1/3)π(4.9)^2h
(3/π) * 226.38 = 4.9^2h
Divide both sides of the equation by (4.9)^2:
(3/π) * 226.38 / (4.9)^2 = h
5. Calculating the height:
Using a calculator, evaluate the right side of the equation:
h ≈ 8.9 dm
Therefore, the height of the conical vessel is approximately 8.9 dm, which is closest to option 'C' (9 dm).
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The area of base of a conical vessel is 75.46 dm2and its volume is 226.38 dm3. The height of the conical vessel isa)15 dmb)6 dmc)9 dmd)12 dmCorrect answer is option 'C'. Can you explain this answer?
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The area of base of a conical vessel is 75.46 dm2and its volume is 226.38 dm3. The height of the conical vessel isa)15 dmb)6 dmc)9 dmd)12 dmCorrect answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The area of base of a conical vessel is 75.46 dm2and its volume is 226.38 dm3. The height of the conical vessel isa)15 dmb)6 dmc)9 dmd)12 dmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of base of a conical vessel is 75.46 dm2and its volume is 226.38 dm3. The height of the conical vessel isa)15 dmb)6 dmc)9 dmd)12 dmCorrect answer is option 'C'. Can you explain this answer?.
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