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A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:
- a)6
- b)4
- c)2
- d)5
- e)3
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A solid cube of side 8 cm is dropped into a rectangular container of l...
The volume of cube = The volume of the rectangular container with a length of 16 cm, breadth of 8 cm, and height of the water level rise
Let, the height of the water level will rise = x cm
So, 83 = 16 × 8 × x
⇒ 512 = 128 × x
⇒ x = 512/128 = 4
∴ The rise of water level (in cm) is 4 cm
Most Upvoted Answer
A solid cube of side 8 cm is dropped into a rectangular container of l...
The volume of cube = The volume of the rectangular container with a length of 16 cm, breadth of 8 cm, and height of the water level rise
Let, the height of the water level will rise = x cm
So, 83 = 16 × 8 × x
⇒ 512 = 128 × x
⇒ x = 512/128 = 4
∴ The rise of water level (in cm) is 4 cm
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Community Answer
A solid cube of side 8 cm is dropped into a rectangular container of l...
Given:
- Side of the cube = 8 cm
- Length of the container = 16 cm
- Breadth of the container = 8 cm
- Height of the container = 15 cm
To find:
The rise of water level when the cube is dropped into the container.
Solution:
When the cube is dropped into the container, it displaces a certain volume of water. This displacement causes the water level to rise.
Step 1: Calculate the volume of the cube:
The volume of a cube is given by the formula:
Volume = (side)^3
Substituting the given value of the side:
Volume = (8 cm)^3 = 512 cm^3
Step 2: Calculate the volume of the container:
The volume of a rectangular container is given by the formula:
Volume = length x breadth x height
Substituting the given values of length, breadth, and height:
Volume = 16 cm x 8 cm x 15 cm = 1920 cm^3
Step 3: Calculate the rise of water level:
The rise of water level is equal to the volume of the cube divided by the base area of the container.
The base area of the container is given by the formula:
Base Area = length x breadth
Substituting the given values of length and breadth:
Base Area = 16 cm x 8 cm = 128 cm^2
Now, we can calculate the rise of water level using the formula:
Rise of water level = Volume of cube / Base Area of container
Substituting the calculated values:
Rise of water level = 512 cm^3 / 128 cm^2 = 4 cm
Therefore, the rise of water level when the cube is dropped into the container is 4 cm.
Hence, the correct answer is option B) 4.
- Side of the cube = 8 cm
- Length of the container = 16 cm
- Breadth of the container = 8 cm
- Height of the container = 15 cm
To find:
The rise of water level when the cube is dropped into the container.
Solution:
When the cube is dropped into the container, it displaces a certain volume of water. This displacement causes the water level to rise.
Step 1: Calculate the volume of the cube:
The volume of a cube is given by the formula:
Volume = (side)^3
Substituting the given value of the side:
Volume = (8 cm)^3 = 512 cm^3
Step 2: Calculate the volume of the container:
The volume of a rectangular container is given by the formula:
Volume = length x breadth x height
Substituting the given values of length, breadth, and height:
Volume = 16 cm x 8 cm x 15 cm = 1920 cm^3
Step 3: Calculate the rise of water level:
The rise of water level is equal to the volume of the cube divided by the base area of the container.
The base area of the container is given by the formula:
Base Area = length x breadth
Substituting the given values of length and breadth:
Base Area = 16 cm x 8 cm = 128 cm^2
Now, we can calculate the rise of water level using the formula:
Rise of water level = Volume of cube / Base Area of container
Substituting the calculated values:
Rise of water level = 512 cm^3 / 128 cm^2 = 4 cm
Therefore, the rise of water level when the cube is dropped into the container is 4 cm.
Hence, the correct answer is option B) 4.
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A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:a)6b)4c)2d)5e)3Correct answer is option 'B'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:a)6b)4c)2d)5e)3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:a)6b)4c)2d)5e)3Correct answer is option 'B'. Can you explain this answer?.
A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:a)6b)4c)2d)5e)3Correct answer is option 'B'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:a)6b)4c)2d)5e)3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:a)6b)4c)2d)5e)3Correct answer is option 'B'. Can you explain this answer?.
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