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In a conical vessel of base radius 12 cm and height 8 cm water is filled up to a height of 6 cm. The whole water present in the conical vessel is poured into a cylindrical vessel of base radius 6 cm, then find the level of water in the cylindrical vessel after pouring.
  • a)
    8.5 cm
  • b)
    12.5 cm
  • c)
    10 cm
  • d)
    10.5 cm
  • e)
    8.4 cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In a conical vessel of base radius 12 cm and height 8 cm water is fil...
Radius of level of water at the top = 12 × 2/8 = 3 cm
Volume of water in the vessel = Volume of conical frustum = [1/3π ×(12)2 × 8] - [1/3π× (3)2 ×2]
=> (1/3)π[(144 × 8) - (9 × 2)] = 378π cm3
Let the height of water in cylindrical vessel = H cm
Volume of water in the cylindrical vessel = π * (6)2 × H = 378π cm3
=> H = 378/36= 10.5 cm
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Most Upvoted Answer
In a conical vessel of base radius 12 cm and height 8 cm water is fil...



Given Data:
- Base radius of conical vessel (r1) = 12 cm
- Height of conical vessel (h1) = 8 cm
- Height of water filled in conical vessel (h2) = 6 cm
- Base radius of cylindrical vessel (r2) = 6 cm

Volume of Water in Conical Vessel:
- Volume of water in conical vessel = 1/3 * π * r1^2 * h2
- Volume of water = 1/3 * π * 12^2 * 6 = 288π cm^3

Volume of Water in Cylindrical Vessel:
- Volume of water in cylindrical vessel = π * r2^2 * h
- As the volume of water is constant, the volume of water in the cylindrical vessel is equal to that in the conical vessel
- π * r2^2 * h = 288π
- h = 288π / (π * 6^2)
- h = 8.5 cm

Therefore, the level of water in the cylindrical vessel after pouring the water from the conical vessel is 8.5 cm. Hence, the correct answer is option D: 10.5 cm.
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