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?

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? Correct Answer h = H/2

Calculation:

Let r and h be the radius and height of the new cone.

Volume of new cone = (1/3) × π ×  r2 × h

⇒ 12.5% of the volume of the old cone

⇒ (1/8) × (1/3) × π × R2 × H      ---(1)

Also, since the new cone created from the old cone.

⇒ r/h = R/H

⇒ r = Rh/H

∴ Volume of new cone = (1/3) × π × (Rh/H)2 × h

⇒ (1/3) × π × (R2/H2) × h3      ---(2)

Using (1) and (2)

⇒ H3/8 = h3

⇒ h = H/2

Additional Information

The surface area of a circular cone = πr(l + r)   where l is the slant height and r is the radius of the circular base.

Bissoy MCQ

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. 
 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 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.
A right circular cone cut by a plane parallel to its base. The volume of the newly formed two pieces differs by 100 cc. If the volume and height of the older cone is 700 cc and 70 cm, what will be the height of the newly formed 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.
From a large cone of volume 600 cm3, a small cone is cut whose height is 70% of the height of the large cone. If the radius of the small cone is 50% of the radius of the large cone, then find the volume of the remaining part left after cutting the small 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.
A right circular cone of base radius 15 cm and height 40 cm is cut parallel to its base so as to obtain a frustum of height 10 cm and volume of 2000π cm3. What is the radius of the upper base of the frustum?
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 :