Bissoy.com
Doctors Medicines MCQs Q&A

A person has 3 containers (cylindrical, spherical, and hemispherical) full of water. The radius of each container is equal and the height of the cylindrical container is 14 m. If the volume of the cylindrical container is 396 m3 and water from all three containers is put in the big cuboidal container whose length and breadth is 20 m and 12 m. How much water rises in a cuboidal container?

A person has 3 containers (cylindrical, spherical, and hemispherical) full of water. The radius of each container is equal and the height of the cylindrical container is 14 m. If the volume of the cylindrical container is 396 m3 and water from all three containers is put in the big cuboidal container whose length and breadth is 20 m and 12 m. How much water rises in a cuboidal container? Correct Answer 33/14 m 

Given:

Radius of cylinder, sphere, and hemisphere is equal

Height of cylindrical vessel = 14 m

Volume of cylindrical vessel = 396 m3

Formula used:

Volume of cylinder = πr2h

Volume of sphere = 4/3 π r3

Volume of hemisphere = 2/3 π r3

Calculation:

Volume of the cylinder = π × R2 × H

⇒ 396 = (22/7) × R2 × 14

⇒ R2 = (396 × 7)/ (14 × 22)

⇒ R = 3 m

Radius of each container = 3 m

Total volume of water in all three container = volume of water in the cuboidal container

Volume of cylinder + volume of sphere + volume of hemisphere = l × b × h

⇒ π × 3 × 3 × 14 + (4/3) × π × 3 × 3 × 3 + (2/3) × π × 3 × 3 × 3 = 20 × 12 × h

⇒ 9π (14 + 4 +2) = 20 × 12 × h

⇒ 9π = 12 × h

⇒ h = 33/14

∴ Water rise in cuboidal container = 33/14 m 

Related Questions

“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. 
Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relation among the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. The options represent the relations among three quantities. A. < B. > C. ≤ D. ≥ E. = Quantity 1: There is a square field of side 4 meter. A flower bed is to be prepared in its centre, leaving a gravelled path of uniform length around the flowerbed. The cost of preparing the flowerbed and gravelling the path is Rs. 100 and Rs. 200 per square meter respectively. If the total cost is Rs. 1756 then find the double of  width of gravelled path. Quantity 2: The height of a cone is 45 cm. A small cone is cut from it parallel to the base. If the ratio of volume of small cone and the remaining part is 8 : 19 then what is the height from the base from where the cone was cut? Quantity 3: A cylindrical container of radius 60 cm and height 150 cm is filled with ice cream. 10 cones of equal volume need to be prepared from the whole ice-cream. These cones has hemispherical top and the height of the conical portion is 4 times the radius of hemisphere. Find radius of the hemisphere. 
Given below are two quantities named A and B. Based on the given information, you have to determine relation between the two quantities. You should use the given data and knowledge of Mathematics to choose between the possible answers. Quantity A: Number of hemispheres that can be formed by melting a sphere having volume equal to the volume of right circular cylinder whose diameteris 6 cm and height is 4 cm. Also, radius of hemisphere formed is half the radius of sphere from which the hemisphere is formed. Quantity B: Number of ice cream cones that can be made from a right circular cylinder shape ice cream container having radius 6 cm and height 5 cm. Ice cream cone to be made should have height 4 cm and slant height 5 cm and there should be a hemisphere made on top of the cone having radius equal to the radius of cone.
The average of the height of the 20 employee of the company is 1.5 m.In the month of June, two employees named Rita and Sumit left the company whose height are 1.4 m and 1.6 m respectively. In August, two more people left the company whose average of height is 1.7 m and one person join the company whose height is 87.5% of height of Sumit. Before the December, more four people left the company whose height are 1.3 m, 1.1 m, 1.32 m and 1.25 m respectively and more 5 people join the company whose height are 1.26 m, 1.18 m, 1.39 m and 1.4 m respectively. The average of height in the month of September is ….
A cylindrical can of internal diameter 14 m and of height 10 m is used to store water. The cylindrical can is half filled with water and that water is poured into another cylinder which is mounted on hemispherical bowl. The cylinder is 5/6th filled. The radius of cylindrical and spherical part is 3/10th of the radius of can. Find the height of the can.
If the radius of the new hemispherical container is tripled of that of the radius of the old hemispherical container, then find the ratio of the volume of the new container to the old container.
Some small cubes of same height 7 cm but variable length and width are put inside a large cuboid of height 21 cm. Length and width of cuboid is 32 cm and 24 cm, respectively. Small cubes are put such that cubes at the bottom most layer is of similar base area; second layer contains all the cubes of similar base area and third layer have all the cubes of similar base area. Which of the following statement(s) given below is / are TRUE? A: If side of each small cubes at bottom most layer is 8 cm, then maximum number of small cubes that can be put at bottom most layer is 12. B: If maximum of 48 cubes can be put at second layer, then side of each cube at second layer is 6 cm. C: If side of each small cubes at third layer is 1.6 cm, then maximum number of small cubes that can be put at third layer is 300.
Three containers whose volumes are in the ratio of 2 : 3 : 4 are full of mixture of spirit and water. In the 1st container the ratio of spirits and water is 4 : 1, in 2nd container the ratio is 11 : 4 and on the 3rd container ratio is 7 : 3. All the three mixtures are mixed in a big container. The ratio of spirit and water in the resultant mixture is ?
The internal length and breadth of a cuboidal store are 16 m and 13 m respectively and its height is 11 m. There is another cubical store whose internal length, breadth and height are 8 m each. How many total cubical boxes each of side one metre can be placed in these two stores to a height of 7 metres?
A solid cylindrical rod whose height is 9 times of its radius is melted and recast into spherical balls whose radius is half of the cylindrical radius. Then, number of spherical balls will be –