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Two cylindrical buckets – A and B – contain only water. Three-fourths of bucket A’s volume is occupied by water while one-fourths of bucket B’s volume is occupied by water, When all the water in bucket A is poured into bucket B, bucket B gets exactly half-filled. If the radius of the base area of bucket A is twice the radius of base area of bucket B, and the height of bucket B is 2 metres, what is the height of the container A in metres?
- a)1/24
- b)1/6
- c)1/4
- d)1/3
- e)1/2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Two cylindrical buckets – A and B – contain only water. Th...
Step 1: Question statement and Inferences
Let the radius, height and volume of bucket A be r, h and v. Let the radius, height and volume of bucket B be R, H and V.
Since three-fourths of bucket A raises the volume of bucket B rise from one-fourths to one-half of its volume,
ividing both sides of the equation by , we get
Step 2: Finding required values
We also know that r = 2R and H = 2. Substituting these values and, we have
Step 3: Calculating the final answer
Dividing both sides by R2, we obtain
Correct Answer : B
Most Upvoted Answer
Two cylindrical buckets – A and B – contain only water. Th...
Understanding Bucket A and Bucket B
- Let the radius of bucket B be r and its height be h = 2 metres.
- Therefore, the volume of bucket B (V_B) can be calculated as:
V_B = πr²h = πr²(2) = 2πr².
Water in Bucket B
- Since one-fourth of bucket B is occupied by water, the volume of water in bucket B (W_B) is:
W_B = (1/4) * V_B = (1/4) * 2πr² = (1/2)πr².
Water from Bucket A
- The radius of bucket A is 2r (twice that of bucket B).
- Let the height of bucket A be H.
- The volume of bucket A (V_A) is:
V_A = π(2r)²H = 4πr²H.
- Three-fourths of bucket A is filled with water, so the volume of water in bucket A (W_A) is:
W_A = (3/4) * V_A = (3/4) * 4πr²H = 3πr²H.
Combining the Water
- When all the water from bucket A is poured into bucket B, bucket B becomes half-filled.
- The volume of water when bucket B is half-filled is:
(1/2) * V_B = (1/2) * 2πr² = πr².
Setting Up the Equation
- The total water in bucket B after pouring from A is:
W_A + W_B = πr².
- Plugging in the values:
3πr²H + (1/2)πr² = πr².
Simplifying
- We can cancel πr² from all terms:
3H + 1/2 = 1.
- Rearranging gives:
3H = 1 - 1/2 = 1/2,
H = (1/2) / 3 = 1/6.
Conclusion
- The height of container A is therefore:
H = 1/6 metres.
Thus, the correct answer is option 'B'.
- Let the radius of bucket B be r and its height be h = 2 metres.
- Therefore, the volume of bucket B (V_B) can be calculated as:
V_B = πr²h = πr²(2) = 2πr².
Water in Bucket B
- Since one-fourth of bucket B is occupied by water, the volume of water in bucket B (W_B) is:
W_B = (1/4) * V_B = (1/4) * 2πr² = (1/2)πr².
Water from Bucket A
- The radius of bucket A is 2r (twice that of bucket B).
- Let the height of bucket A be H.
- The volume of bucket A (V_A) is:
V_A = π(2r)²H = 4πr²H.
- Three-fourths of bucket A is filled with water, so the volume of water in bucket A (W_A) is:
W_A = (3/4) * V_A = (3/4) * 4πr²H = 3πr²H.
Combining the Water
- When all the water from bucket A is poured into bucket B, bucket B becomes half-filled.
- The volume of water when bucket B is half-filled is:
(1/2) * V_B = (1/2) * 2πr² = πr².
Setting Up the Equation
- The total water in bucket B after pouring from A is:
W_A + W_B = πr².
- Plugging in the values:
3πr²H + (1/2)πr² = πr².
Simplifying
- We can cancel πr² from all terms:
3H + 1/2 = 1.
- Rearranging gives:
3H = 1 - 1/2 = 1/2,
H = (1/2) / 3 = 1/6.
Conclusion
- The height of container A is therefore:
H = 1/6 metres.
Thus, the correct answer is option 'B'.
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Two cylindrical buckets – A and B – contain only water. Three-fourths of bucket A’s volume is occupied by water while one-fourths of bucket B’s volume is occupied by water, When all the water in bucket A is poured into bucket B, bucket B gets exactly half-filled. If the radius of the base area of bucket A is twice the radius of base area of bucket B, and the height of bucket B is 2 metres, what is the height of the container A in metres?a)1/24b)1/6c)1/4d)1/3e)1/2Correct answer is option 'B'. Can you explain this answer?
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Two cylindrical buckets – A and B – contain only water. Three-fourths of bucket A’s volume is occupied by water while one-fourths of bucket B’s volume is occupied by water, When all the water in bucket A is poured into bucket B, bucket B gets exactly half-filled. If the radius of the base area of bucket A is twice the radius of base area of bucket B, and the height of bucket B is 2 metres, what is the height of the container A in metres?a)1/24b)1/6c)1/4d)1/3e)1/2Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Two cylindrical buckets – A and B – contain only water. Three-fourths of bucket A’s volume is occupied by water while one-fourths of bucket B’s volume is occupied by water, When all the water in bucket A is poured into bucket B, bucket B gets exactly half-filled. If the radius of the base area of bucket A is twice the radius of base area of bucket B, and the height of bucket B is 2 metres, what is the height of the container A in metres?a)1/24b)1/6c)1/4d)1/3e)1/2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cylindrical buckets – A and B – contain only water. Three-fourths of bucket A’s volume is occupied by water while one-fourths of bucket B’s volume is occupied by water, When all the water in bucket A is poured into bucket B, bucket B gets exactly half-filled. If the radius of the base area of bucket A is twice the radius of base area of bucket B, and the height of bucket B is 2 metres, what is the height of the container A in metres?a)1/24b)1/6c)1/4d)1/3e)1/2Correct answer is option 'B'. Can you explain this answer?.
Two cylindrical buckets – A and B – contain only water. Three-fourths of bucket A’s volume is occupied by water while one-fourths of bucket B’s volume is occupied by water, When all the water in bucket A is poured into bucket B, bucket B gets exactly half-filled. If the radius of the base area of bucket A is twice the radius of base area of bucket B, and the height of bucket B is 2 metres, what is the height of the container A in metres?a)1/24b)1/6c)1/4d)1/3e)1/2Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Two cylindrical buckets – A and B – contain only water. Three-fourths of bucket A’s volume is occupied by water while one-fourths of bucket B’s volume is occupied by water, When all the water in bucket A is poured into bucket B, bucket B gets exactly half-filled. If the radius of the base area of bucket A is twice the radius of base area of bucket B, and the height of bucket B is 2 metres, what is the height of the container A in metres?a)1/24b)1/6c)1/4d)1/3e)1/2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cylindrical buckets – A and B – contain only water. Three-fourths of bucket A’s volume is occupied by water while one-fourths of bucket B’s volume is occupied by water, When all the water in bucket A is poured into bucket B, bucket B gets exactly half-filled. If the radius of the base area of bucket A is twice the radius of base area of bucket B, and the height of bucket B is 2 metres, what is the height of the container A in metres?a)1/24b)1/6c)1/4d)1/3e)1/2Correct answer is option 'B'. Can you explain this answer?.
Solutions for Two cylindrical buckets – A and B – contain only water. Three-fourths of bucket A’s volume is occupied by water while one-fourths of bucket B’s volume is occupied by water, When all the water in bucket A is poured into bucket B, bucket B gets exactly half-filled. If the radius of the base area of bucket A is twice the radius of base area of bucket B, and the height of bucket B is 2 metres, what is the height of the container A in metres?a)1/24b)1/6c)1/4d)1/3e)1/2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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