Please refer to the following lecture notes for the formulas used in this exercise: Notes

Question 1: A solid sphere of radius is melted and recast into solid right circular cones of radius and height Calculate the number of cones recast. **[2013]**

Answer:

Sphere: Radius

Cone: Radius and Height

Question 2: A hollow sphere of internal and external diameters and respectively is melted into a cone of base diameter Find the height of the cone. **[2002]**

Answer:

Internal diameter Internal radius

External diameter External radius

Radius of the

Question 3: The radii of the internal and external surfaces of a metallic spherical shell are and respectively. It is melted and recast into a solid right circular cone of height Find the diameter of the base of the cone.

Answer:

Internal radius

External radius

Height of the cone

Therefore and hence diameter

Question 4: Total volume of three identical cones is the same as that of a bigger cone whose height is and diameter Find the radius of the base of each smaller cone, if height of each is

Answer:

Let the radius of the cone

Height of the cone

Bigger cone: Height and radius

Question 5: A solid rectangular block of metal by by is melted and formed into a solid sphere. Calculate the radius of the sphere.

Answer:

Dimension of the block

Let the radius of the sphere

Question 6: A hemispherical bowl of internal radius is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter and height How many containers are necessary to empty the bowl?

Answer:

Bowl: Internal radius

Cone: radius , Height

Question 7: A hemispherical bowl of diameter is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius Find the height of the cone if it is completely filled. [2010]

Answer:

Hemisphere: Radius

Cone: Radius , Height

Question 8: A solid cone of radius and height is melted and made into small spheres of radius Find the number of spheres formed. **[2011]**

Answer:

Cone: Radius , Height

Sphere: Radius

Question 9: The total area of a solid metallic sphere is It is melted and recast into solid right circular cones of radius and height Calculate: (i) the radius of the solid sphere, (ii) the number of cones recast. **[2000]**

Answer:

Surface area

(i)

(ii) Cone: Radius , Height

Question 10: A solid metallic cone, with radius and height , is made of some heavy metal A. In order to reduce its weight, a conical hole is made in the cone as, shown and it is completely filled with a lighter metal B. The conical hole has a diameter of and depth calculate the ratio of the volume of metal A to the volume of the metal B in the solid.

Answer:

Cone: Radius , Height

Conical hole: Radius , Height

Question 11: A hollow sphere of internal and external and respectively is melted and recast into small cones of base radius and height Find the number of cones. **[2012]**

Answer:

Sphere: Internal radius , External radius

Cone: Radius , Height

Question 12: The surface area of a solid metallic sphere is It is melted and recast into solid right circular cones of radius and height Calculate: (i) the radius of the sphere (ii) the number of cones recast. (Take )** [2014]**

Answer:

Surface area of sphere

Cone: Radius , Height

Hence