Bissoy.com
Doctors Medicines MCQs Q&A

A conical vessel of radius 7 cm and height 30 cm is completely filled with a liquid. From it, the liquid is poured into several conical vessels of radius 5 cm and height 21 cm, thereby filling them completely. What part of the last conical vessel will remain empty? Use π = 22/7.

A conical vessel of radius 7 cm and height 30 cm is completely filled with a liquid. From it, the liquid is poured into several conical vessels of radius 5 cm and height 21 cm, thereby filling them completely. What part of the last conical vessel will remain empty? Use π = 22/7. Correct Answer 1/5

As we know, a cone with radius ‘r’ and height ‘h’, has a volume = 1/3 πr2h

Total volume of liquid = volume of first conical vessel = (1/3) × (22/7) × (7)2 × 30 = 1540 cm3

Volume of liquid poured in one vessel = volume of second conical vessel

= (1/3) × (22/7) × (5)2 × 21 = 550 cm3

Total number of vessels filled = 1540/550 = 2.8

Hence, the third vessel is only filled = 0.8 = 80%

∴ The last vessel remained empty by = 100 – 80 = 20% = 1/5

Related Questions

There are two vessels A and B. Vessel A is containing 60L of Pure milk and vessel B is containing 28L of pure water. From vessel A, 8L of milk is taken out and poured into vessel B. Then, 6L of mixture (milk and water) is taken out from vessel B and poured into vessel A. What is the ratio of the quantity milk in vessel A to the quantity of pure water in vessel B?
An empty vessel was first filled with alcohol. When the vessel got 1/4th empty, it was filled with spirit. Again, when the vessel got 1/3rd empty, it was filled with alcohol. Again when the vessel got 1/5th empty, it was filled with spirit. Find the percentage of spirit in the vessel.
Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. What is the ratio of coconut oil and milk in the final beaker? If contents from four vessels poured in it. I. Vessel B has 10 ml more capacity than vessel A and the ratio of coconut oil and milk in vessel B is 2 ∶ 7. Vessel C has coconut oil and milk in the ratio 2 ∶ 3 and contains 38 ml more capacity than Vessel D II. Vessel A has milk and coconut oil in the ratio 3 ∶ 5. Vessel C has 12 ml more coconut oil than vessel D.
2 vessels V1 and V2 contain liquids of different prices and with volumes 160 and 40 litres respectively. Equal quantities are drawn from both, such that the liquid drawn from V1 is poured into V2 and liquid drawn from V2 is poured into V1. Thus, the price/litre becomes equal in both Vessels. What is the quantity that was drawn from both the vessels?
A tank has an optional adjustable outlet pipe that can be attached to the tank at any height we want. This outlet pipe drains water from the tank at a constant rate, while the tank is being filled using another inlet pipe at a constant rate. If the outlet, pipe is attached at half the height of the tank, the tank, which is initially empty gets filled in 18 hours. If the outlet pipe is attached at height equal to two third height of the tank, the tank, which is initially empty, is filled in 16 hours. In how many hours will the tank, which is initially empty, be completely filled if the outlet pipe is not attached to the tank?
A conical vessel whose internal base radius is 18 cm and height 60 cm are full of a liquid. The entire liquid of the vessel is emptied into a cylindrical vessel with an internal radius of 15 cm. The height (in cm) to which the liquid rises in the cylindrical vessel is:
Two vessels a and b of the equal volume contain milk and water in the ratio 3 ∶ 2 and 2 ∶ 1 respectively. Two liters of the solution from the vessel a and three liters of the solution from vessel b are poured in a big empty vessel c. If the solution in c occupied 40% of the capacity of c, what proportion of the volume of vessel c should be the volume of water that shall be added so that the ratio of milk and water in vessel c becomes 1 ∶ 1?
Three vessels of equal capacity are filled with a solution of alcohol and water. The ratio of alcohol and water in the first vessel is 2 ∶ 3, in the second vessel is 3 ∶ 4 , and in the third vessel is 4 ∶ 5. The solution of these 3 vessels is mixed into a bigger vessel. What is the ratio of alcohol to water in the bigger vessel?
A conical vessel is full of water with radius 10 cm and height 54 cm. The water of the vessel poured into a cylindrical vessel having the base radius 15 cm. What will be the depth of the water in the cylindrical vessel? (Assume no water wasted)
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m.