7.5 Conversion of Solids from one shape to another with no change in Volume

. Conversion of Solids from one shape to another with no change in Volume Conversions or Transformations becomes a common part of our daily life. For example, a gold smith melts a bar of gold to transform it to a jewel. Similarly, a kid playing with clay shapes it into different toys, a carpenter uses the wooden logs to form different house hold articles/furniture. Likewise, the conversion of solids from one shape to another is required for various purposes. In this section we will be learning problems involving conversions of solids from one shape to another with no change in volume. Example . A metallic sphere of radius cm is melted and recast into small spheres each of radius cm. How many small spheres can be obtained? Solution Let the number of small spheres obtained be n . Let r be the radius of each small sphere and R be the radius of metallic sphere. Here, R = cm, r = cm Now, n ´ (Volume of a small sphere) = Volume of big metallic sphere  = p R n = n = ⇒ n = Therefore, there will be small spheres. Example . A cone of height cm is made up of modeling clay. A child reshapes it in the form of a cylinder of same radius as cone. Find the height of the cylinder. Solution Let h and h be the heights of a cone and cylinder respectively. Also, let r be the raius of the cone. Given that, height of the cone h cm; radius of the cone and cylinder r = cm Since, Volume of cylinder = Volume of cone p r h = p r h h = ´ h ⇒ h = Therefore, height of cylinder is cm Example . A right circular cylindrical container of base radius cm and height cm is full of ice cream. The ice cream is to be filled in cones of