Bissoy.com
Doctors Medicines MCQs Q&A

A right circular cone is put inside a cylinder. The diameter and height of the cylinder is equal to that of the cone. Find the volume of air that is outside the cone but inside the cylinder. 

A right circular cone is put inside a cylinder. The diameter and height of the cylinder is equal to that of the cone. Find the volume of air that is outside the cone but inside the cylinder.  Correct Answer 2/3 volume of cylinder

Solution:

Given:

Diameter of cone = diameter of cylinder

Height of cone = height of cylinder

Concept:

Volume of air outside cone but inside cylinder should be equal to the difference between the volume of cylinder and the cone.

If diameters are equal radius are also equal.

Formula:

Volume of cylinder = πr2h

Volume of cone = 1/3πr2h

Calculation:

Let the radius be r, height be h.

Difference between volume of cylinder and volume of cone = πr2h – 1/3πr2h

⇒Difference between volume of cylinder and volume of cone = 2/3πr2h

∴ Volume of air outside cone and inside cylinder = 2/3 volume of cylinder

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. 
Let X be a right circular cylinder with height ‘h’ and diameter ‘d’, Y be a right circular cone with height and diameter equal to that of cylinder X and Z be a sphere of maximum volume that can be inscribed in the cylinder X. Consider the following statements: 1. If d < h, then the volume of Y is (h/2d) times the volume of Z. 2. If d > h, then the volume of Y is (d2/2h2) times the volume of Z. Which of the above statements is/are correct?
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 sum and difference of the slant height and height of cone A are in the ratio 3 ∶ 1, while the sum and difference of the slant height and height of cone Y are in the ratio 5 ∶ 1. If the volume of cone A is 30% of the volume of cone B, then the height of cone A is what percentage of the height of cone B.
The volume of a right circular cone is equal to the volume of that right circular cylinder whose height is 27 cm and diameter of its base is 30 cm. If the height of the cone is 25 cm, then what will be the diameter of its base?
A right circular cone of whose height and radius are equal is put above a right circular cylinder of height 7 cm and radius 9 cm such that base of cone and cylinder matches perfectly. Find the total volume of shape.
A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. Consider the following statements: 1) The surface area of the sphere is √5 Times the curved surface area of the cone. 2) The surface area of the cube is equal to the curved surface area of the cylinder. Which of the above statements is/are correct?
A cylinder has a 28 m diameter and height is 25% of the diameter of the cylinder then find the difference between the volume of the cylinder and the volume of a cone whose height is 150% of the radius of the cylinder and whose radius is 50% of the height of the cylinder.
 The following question has two statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.  The height of a right circular cone is ‘h’ and radius is ‘r’. A small cone is cut-off at the top by a plane parallel to the base. At what height above the base, the section has been made? I) Height of cone (h) = 40 cm II) Volume of smaller cone ∶ volume of larger cone = 1 ∶ 30
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.