Bissoy.com
Doctors Medicines MCQs Q&A

A hemispherical bowl of internal radius 18 cm contains a liquid. The liquid is filled in small cylindrical bottles of internal radius 3 cm and internal height 4 cm. What is the number of bottles used to empty the bowl ?

A hemispherical bowl of internal radius 18 cm contains a liquid. The liquid is filled in small cylindrical bottles of internal radius 3 cm and internal height 4 cm. What is the number of bottles used to empty the bowl ? Correct Answer 108

Given:

Internal radius of hemispherical bowl = 18 cm

Internal radius of bottle = 3 cm

Internal height of bottle = 4 cm

Formula used:

Volume of a hemisphere = (2/3) πR3

Volume of a cylinder = πr2h

R = radius of hemisphere, h = height of the cylinder

r = radius of the cylinder

Calculation:

Total volume of liquid in hemisphere = 2/3 × π ×183 = 3888π cm3

Let the number of bottles be n

Then according to the question:

3888π = n × π × (3)2 × 4

⇒ n = 108

∴ Total number of bottles = 108

Related Questions

A hemispherical bowl of internal diameter 36 cm is full of a liquid. This liquid is to be filled into cylindrical bottles each of radius 3 cm and height 12 cm. How many such bottles are required to empty the bowl?
A hemispherical bowl of internal diameter 72 cm is full of a liquid. This liquid is to be filled into cylindrical bottles each of radius 3 cm and height 12 cm. How many such bottles are required to empty the bowl?
Identical hemispherical bowls of internal diameter 14 cm are to be filled with liquid from a cylindrical tank of internal diameter 40 cm and height 70 cm. If the cylindrical tank is 80% filled with liquid and the hemispherical bowls are to be filled only 75%, then how many bowls will be filled? Use π = 22/7. 
A hemispherical bowl of internal radius 12 cm is full of a liquid. This liquid is to be filled into conical bottles each of radius 6 cm and height 8 cm. How many such bottles are required to empty the bowl?
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.
A hemispherical bowl of internal radius 12 cm contains liquid. This liquid is to be filled into cylindrical container of diameter 4 cm and height 3 cm. The number of containers that is necessary to empty the bowl is :
The price of a bottle of cold drink is Rs. 10. One bottle of cold drink can also be bought by returning 10 empty bottles. A person has Rs. 1,000 and 19 empty bottles. Assuming that the person can consume any number of bottles he buys, what will be the number of empty bottles he possesses at the end if he buys the maximum number of bottles of cold drink and consumes all?
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. 
“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. 
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?