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The volume of a right circular cone, with a base radius the same as its altitude, and the volume of a hemisphere are equal. The ratio of the radii of the cone to the hemisphere is

The volume of a right circular cone, with a base radius the same as its altitude, and the volume of a hemisphere are equal. The ratio of the radii of the cone to the hemisphere is Correct Answer 23\:\1

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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.
What will be the volume of the shape formed by carving out a right circular cone from a hemisphere of radius R cm, such that the volume of the cone is maximum and the base of the hemisphere is the base of the cone. I. Volume of the cone is 9π cm3.  II. Ratio of the total surface area of the cone to the hemisphere is (√2 + 1) : 3.
“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. 
The volume of a right circular cone, whose radius of the base is half of its altitude, and the volume of a hemisphere are equal. The ratio of the radius of the cone to the radius of the hemisphere is
There is a hemisphere hollow from inside in which there is a cone inscribed whose base is the diameter of the hemisphere. If the radius of the hemisphere is 6 cm, then find the ratio of the volume of hemisphere and volume of the remaining part of hemisphere when cone is dug out from it.
A right circular cone of circular base radius R and H resting on a plane. The cone is cut by a plane parallel to the base. The new circular cone-formed has a 12.5% volume of the older cone. What is the height of the new cone?
The radius of a sphere is equal to the radius of the base of a right circular cone, and the volume of the sphere is double the volume of the cone. The ratio of the height of the cone to the radius of its base is :
The volume of a right circular cone, whose radius of the base is same as one-third of its altitude, and the volume of a sphere are equal. The ratio of the radius of the cone to the radius of the sphere is:
The volume of a right circular cone, whose radius of the base is same as one-third of its altitude, and the volume of a sphere are equal. The ratio of the radius of the cone to the radius of the sphere is :