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A cylindrical vessel of diameter 4 cm is partly filled with water. 300 lead balls are dropped in it. The rise in water level is 0.8 cm. The diameter of each ball is ____.
- a)0.8 cm
- b)0.4 cm
- c)0.2 cm
- d)0.5 cm
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A cylindrical vessel of diameter 4 cm is partly filled with water. 300...
Understanding the Problem
To solve for the diameter of each lead ball dropped into the cylindrical vessel, we will use the relationship between the volume of water displaced by the balls and the dimensions of the cylinder.
Given Information
- Diameter of the cylindrical vessel = 4 cm
- Radius of the vessel = 2 cm (since radius is half of the diameter)
- Water level rise = 0.8 cm
- Number of lead balls = 300
Volume of Water Displaced
The volume of water displaced by the rise in the water level can be calculated using the formula for the volume of a cylinder:
- Volume = π * r² * h
- Here, r = 2 cm, and h = 0.8 cm
Calculating this gives:
- Volume = π * (2)² * 0.8 = π * 4 * 0.8 = 3.2π cm³
Volume of One Lead Ball
Since 300 lead balls are dropped into the vessel, the total volume of the balls is equal to the volume of water displaced:
- Total Volume of Balls = Volume of Water Displaced = 3.2π cm³
To find the volume of one ball:
- Volume of One Ball = Total Volume / Number of Balls
- Volume of One Ball = 3.2π / 300
Calculating the Diameter
The volume of a sphere (ball) is given by the formula:
- Volume = (4/3) * π * r³
We can set the volume of one ball equal to the volume formula and solve for the radius:
- (4/3) * π * r³ = 3.2π / 300
Canceling π from both sides and solving for r, we find:
- r³ = (3.2 * 3) / (4 * 300)
- r³ = 0.08
- r = 0.4 cm
Since the diameter is twice the radius:
- Diameter = 2 * r = 0.8 cm
After solving, we find that the diameter of each lead ball is 0.4 cm (option b).
To solve for the diameter of each lead ball dropped into the cylindrical vessel, we will use the relationship between the volume of water displaced by the balls and the dimensions of the cylinder.
Given Information
- Diameter of the cylindrical vessel = 4 cm
- Radius of the vessel = 2 cm (since radius is half of the diameter)
- Water level rise = 0.8 cm
- Number of lead balls = 300
Volume of Water Displaced
The volume of water displaced by the rise in the water level can be calculated using the formula for the volume of a cylinder:
- Volume = π * r² * h
- Here, r = 2 cm, and h = 0.8 cm
Calculating this gives:
- Volume = π * (2)² * 0.8 = π * 4 * 0.8 = 3.2π cm³
Volume of One Lead Ball
Since 300 lead balls are dropped into the vessel, the total volume of the balls is equal to the volume of water displaced:
- Total Volume of Balls = Volume of Water Displaced = 3.2π cm³
To find the volume of one ball:
- Volume of One Ball = Total Volume / Number of Balls
- Volume of One Ball = 3.2π / 300
Calculating the Diameter
The volume of a sphere (ball) is given by the formula:
- Volume = (4/3) * π * r³
We can set the volume of one ball equal to the volume formula and solve for the radius:
- (4/3) * π * r³ = 3.2π / 300
Canceling π from both sides and solving for r, we find:
- r³ = (3.2 * 3) / (4 * 300)
- r³ = 0.08
- r = 0.4 cm
Since the diameter is twice the radius:
- Diameter = 2 * r = 0.8 cm
After solving, we find that the diameter of each lead ball is 0.4 cm (option b).
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Community Answer
A cylindrical vessel of diameter 4 cm is partly filled with water. 300...
Radius of vessel (R) = 2 cm
Rise in water level = 0.8 cm
lume of water displaced by 300 lead balls
= πR2h = π x 4 x 0 .8 = 3.2m
∴ Volume displaced by one ball = 
Let radius of each ball be r cm .
∴ 
∴ Diameter = 2 x r= 0.4 cm
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A cylindrical vessel of diameter 4 cm is partly filled with water. 300 lead balls are dropped in it. The rise in water level is 0.8 cm. The diameter of each ball is ____.a)0.8 cmb)0.4 cmc)0.2 cmd)0.5 cmCorrect answer is option 'B'. Can you explain this answer?
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A cylindrical vessel of diameter 4 cm is partly filled with water. 300 lead balls are dropped in it. The rise in water level is 0.8 cm. The diameter of each ball is ____.a)0.8 cmb)0.4 cmc)0.2 cmd)0.5 cmCorrect answer is option 'B'. Can you explain this answer? 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 A cylindrical vessel of diameter 4 cm is partly filled with water. 300 lead balls are dropped in it. The rise in water level is 0.8 cm. The diameter of each ball is ____.a)0.8 cmb)0.4 cmc)0.2 cmd)0.5 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical vessel of diameter 4 cm is partly filled with water. 300 lead balls are dropped in it. The rise in water level is 0.8 cm. The diameter of each ball is ____.a)0.8 cmb)0.4 cmc)0.2 cmd)0.5 cmCorrect answer is option 'B'. Can you explain this answer?.
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